From <@UBVM.CC.BUFFALO.EDU:owner-LISTSERV@UBVM.CC.BUFFALO.EDU> Wed Feb 8 02:33:48 1995 Received: from netaxs.com (root@netaxs.com [198.69.186.1]) by access.netaxs.com (8.6.9/8.6.9) with ESMTP id CAA27442 for ; Wed, 8 Feb 1995 02:33:48 -0500 Received: from UBVM.cc.buffalo.edu (ubvm.cc.buffalo.edu [128.205.2.1]) by netaxs.com (8.6.9/8.6.9) with SMTP id CAA18157 for ; Wed, 8 Feb 1995 02:33:42 -0500 Message-Id: <199502080733.CAA18157@netaxs.com> Received: from UBVM.CC.BUFFALO.EDU by UBVM.cc.buffalo.edu (IBM VM SMTP V2R2) with BSMTP id 2176; Wed, 08 Feb 95 02:33:26 EST Received: from UBVM.CC.BUFFALO.EDU (NJE origin LISTSERV@UBVM) by UBVM.CC.BUFFALO.EDU (LMail V1.2a/1.8a) with BSMTP id 0655; Wed, 8 Feb 1995 02:33:19 -0500 Date: Wed, 8 Feb 1995 02:33:15 -0500 From: "L-Soft list server at UBVM (1.8a)" Subject: File: "GEODESIC LOG9409" To: "Christopher J. Fearnley" Status: RO ========================================================================= Date: Thu, 1 Sep 1994 06:39:46 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Lee Wood Subject: Re: The "PI without Trig" Monster Re RE my earlier post: >>When I changed the program to produce a slop-sided cylinder [snip] >>instead of a vertical sided cylinder, it worked properly. I see I made a typo. "slop-sided" should have been "slope-sided". =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= Lee Wood | Lee_Wood@sfu.ca | INTJ spoken here. =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= ========================================================================= Date: Thu, 1 Sep 1994 02:19:06 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: John Kirk Organization: Netaxs: Philadelphia local provider Subject: FElt and tensegrity (continued) Robert Read (read@cs.utexas.edu) yesterday answered the question I posted, for which I'm grateful. I've used ellipsis below (I apologize -- read the original) in indicating the part of the answer I'm referring-to: >...FElt...does not allow you to analyse a pre-stressed structure... In my experience with building physical-world models (desktop to architectural in scale) and doing math that derives, describes or specifies their form and behavior, I've come to feel that the special case of no-pre-stressing is too narrow to be very useful. The key question in tensegrity design seems to be the degree of pre-stressing. I guess I should be corresponding with the authors of FElt directly, also, to get what seems like a minor user interface change added. >...subtle limitation of FElt and static structural analysis based on the >stiffness method...when loaded, a structure does not change its >geometry...enough to change any angles... In the class of structures I'm elploring now, symmetry assures that any degree of pre-stressing -- short of element failure -- will not affect the geometric form. It's just that I need to specify where I want to be on the force-vs-stretch elasticity curve of the materials. Also, I'm mostly interested in the non-static analysis facilities of FElt ultimately. i.e. modelling the behavior of the structure under perturbations. >...steel cables...turnbuckles... It looked to me in the FElt documentation, as if one only uses words like "steel" as placeholders in order to refer to somewhere else that one has explicitly specified parameters such as the index of elasticity. I mentioned steel only to be concrete in my question, and in the context of having used steel cable in the larger structures I've built. (I'm thinking of posting scanned photos of physical-world models, in case anyone would be interested in seeing them.) I've never used turnbuckles myself, because my own primary purpose in building structures has been to test whether the mathematical models, from which they were designed, accurately represent the physical reality -- thus eliminating the unknown factors that would be corrected by adjusting turnbuckles. >...using FElt to analyse a tensegrity with cables... I suspect you're using "tensegrity" in a way that is different than the way I use the term. I don't know exactly what the differences are, perhaps broader or narrower in several aspects. I think this is grist for a whole separate thread of discussion. To sum up, I think FElt is a good tool for analysing tensegrity and geodesic-dome-type structures, but the user interface (model specification language only, probably) would have to be modified to allow specification of situations where an element has force applied to it just by the other elements of the structure due to their own elasticity behavior, rather than applied externally. -- John Kirk (215) 382-3040 email: dystan@netaxs.com ========================================================================= Date: Thu, 1 Sep 1994 09:43:55 -0400 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Cal Eastman Subject: Re: Non-synergetics X-To: Geoffrey Wherrett In-Reply-To: <199408291810.OAA03419@hela.INS.CWRU.Edu> although in an "ideal" situation this is true, there are no ideal situations in the real world. This has always been one of teh problems with the scientific method, that theories are based on labratory situations, which are simplifications of the real world. The corallis force indeed does influence water, but the so does the shape of the container and the amount of water turbulance. If you fill a container with water it takes a long time for that water to become "still" enough that the effects of turbulance are not felt. all that having been said... what is meant by the corallis force is, the effect from the force caused by the direction of the spin of the planet. peace Boom shiva mahalinga nataraj :) (puffiness 4evah) On Mon, 29 Aug 1994, Geoffrey Wherrett wrote: > In article , smtc5@uoft02.utoledo.edu > writes: > > >Why does water drain counter-clockwise? > and > What does IMHO mean? > > Water drains counterclockwise due to Coriolis effects. In the Southern > Hemisphere, water drains in the opposite direction. > ========================================================================= Date: Thu, 1 Sep 1994 20:09:00 CDT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Leslie Perelman Subject: Re: Non-synergetics Well, it drains counter-clockwise when viewed from above and clockwise when viewed from below (that is, down under). Seth ========================================================================= Date: Thu, 1 Sep 1994 21:59:50 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: Geodesic sphere algorithm > >- The pentagons are all identical. >- The hexagons are all identical. >- And the triangles which make up a pentagon are isosceles, > but not *quite* equilateral. > >Are all the triangles in a pentagon identical? >i.e. The spokes are all the same length, > but are their chords all the same? > >And for the triangles which make up hexagons: > Are their spokes all the same length? > And their chords? > >If the answer to all the above is "Yes", then >I would agree with you; there probably is only one solution. I'm not positing that the hexagons would all be identical to one another. The only constraint is the number of degrees around each vertex should be the same. ------------------------------------------------ Kirby T. Urner pdx4d@teleport.com 4D Solutions (teleport.com is a public access node) ========================================================================= Date: Thu, 1 Sep 1994 22:03:04 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: Non-synergetics >Geoffrey Wherrett (wherrett@mech.ubc.ca) wrote: > >: In article , smtc5@uoft02.utoledo.edu >: writes: > >: >Why does water drain counter-clockwise? > >: Water drains counterclockwise due to Coriolis effects. In the Southern >Hemisphere, water drains in the opposite direction. > >Only in THEORY, really. The Coriolis effect is quite negligible compared >to other probable effects (geometry of the draining vessel, initial >movement of the water, etc.) I think winds and such larger systems DO >show the effect, but will leave that as an excercise for the reader ;-) > >-- Bob Hiltner >"It is not enough to do well (and I hope you do), you must also do good" > ^^^^ I just came back from southern Africa. My wife shouted for me to come into the kitchen to see how the water was draining in the other direction. Certainly seemed empirically convincing. Everyone check your kitchen sinks and bathtubs, lets see if we all go around in the same direction. No stirring with hands allowed. ------------------------------------------------ Kirby T. Urner pdx4d@teleport.com 4D Solutions (teleport.com is a public access node) ========================================================================= Date: Fri, 2 Sep 1994 17:42:54 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Lee Wood Subject: Re: Geodesic sphere algorithm Kirby wrote, Aug. 29: >The goal is to 'distort' the edges by a hair, longer or shorter, >to cause each vertex to be surrounded by exactly k degrees less >than 360 (k is konstant for all vertices). Furthermore, >k times the number of total vertices will equal 360. I assume >that the 5 spokes of a pentagonal convergence will be the >same length, and arbitrarily make this 1. I'm wondering if >these contraints will now automatically (once the numerical >algorithm is in place) determine the unique chord lengths for >the rest of the sphere. > >Note: computation need only be done for one of the 20 icosa- >sphere's triangles. Would you explain that Note, please. At the time, I assumed that instead of "triangles", you meant "hexagons". i.e. "Note: computation need only be done for one of the 20 icosa- sphere's hexagons." But in light of what you wrote Sept. 1, that would not appear to be the case: >I'm not positing that the hexagons would all be identical >to one another. The only constraint is the number of >degrees around each vertex should be the same. --==o==-- But, in any case, would you please confirm whether I have correctly understood what you've said about deforming a hexagon by altering the lengths of its struts, so that all together, they form a sphere: I have a geodesic sphere model composed of 20 hexagons and 12 pentagons. (The manufacturer neglected to specify exactly what kind of construct it was, but I've assumed it to be an icosa-sphere.) Around this model I count 92 vertices. This means that each vertex must be 720/92=7.826 degrees less than 360. So, in general, the algorithm need only search through strut lengths which result in hexagons whose central vertex is 352.174 degrees. This will cause the hexagon to form a shallow, hexagonal pyramid, whose apex is aproximately 25 degrees. =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= Lee Wood | Lee_Wood@sfu.ca | INTJ spoken here. =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= ========================================================================= Date: Fri, 2 Sep 1994 15:33:43 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: smtc5@UOFT02.UTOLEDO.EDU Organization: University of Toledo Subject: Re: Non-synergetics In Article <199409020503.WAA13807@teleport.com> Kirby Urner writes: >>Geoffrey Wherrett (wherrett@mech.ubc.ca) wrote: >> >>: In article , smtc5@uoft02.utoledo.edu >>: writes: >> >>: >Why does water drain counter-clockwise? >> >>: Water drains counterclockwise due to Coriolis effects. In the Southern >>Hemisphere, water drains in the opposite direction. >> >>Only in THEORY, really. The Coriolis effect is quite negligible compared >>to other probable effects (geometry of the draining vessel, initial >>movement of the water, etc.) I think winds and such larger systems DO >>show the effect, but will leave that as an excercise for the reader ;-) >> >>-- Bob Hiltner >>"It is not enough to do well (and I hope you do), you must also do good" >> ^^^^ > >I just came back from southern Africa. My wife shouted for me >to come into the kitchen to see how the water was draining in >the other direction. Certainly seemed empirically convincing. >Everyone check your kitchen sinks and bathtubs, lets see if >we all go around in the same direction. No stirring with hands >allowed. I tested it. It always drains counter-clockwise even if swished around the opposite direction with your hands (it switches part way through.) Steve Mather ========================================================================= Date: Fri, 2 Sep 1994 20:59:23 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: Geodesic sphere algorithm >Kirby wrote, Aug. 29: >>The goal is to 'distort' the edges by a hair, longer or shorter, >>to cause each vertex to be surrounded by exactly k degrees less >>than 360 (k is konstant for all vertices). Furthermore, >>k times the number of total vertices will equal 360 [720!]. I assume >>that the 5 spokes of a pentagonal convergence will be the >>same length, and arbitrarily make this 1. I'm wondering if >>these contraints will now automatically (once the numerical >>algorithm is in place) determine the unique chord lengths for >>the rest of the sphere. >> >>Note: computation need only be done for one of the 20 icosa- >>sphere's triangles. > >Would you explain that Note, please. At the time, I assumed that >instead of "triangles", you meant "hexagons". Sorry, I wasn't being clear. A spherical icosahedron can be divided into 20 triangular sectors, drawing boundary lines from each pentagon to its nearest neighbors. I was supposing my construct would have the same symmetry as a Class I geodesic sphere, in which case each of the 20 sectors would be identical. The hexagonal pattern is *internal* to each of these larger districts (1/20 of the total sphere each). As Chris pointed out, even computing for an entire sector would be redundant, since the pattern growing out from any of the 3 pentagons at its corners would be the same towards the middle of the sector. Only a subregion of the sector needs to be computed. __ / \ <-- subdivides into 6 triangles with the addition of \__/ 6 "spokes" "rim" >i.e. >"Note: computation need only be done for one of the 20 icosa- >sphere's hexagons." > >But in light of what you wrote Sept. 1, that would not appear >to be the case: >>I'm not positing that the hexagons would all be identical >>to one another. The only constraint is the number of >>degrees around each vertex should be the same. > >--==o==-- > >But, in any case, would you please confirm whether I have correctly >understood what you've said about deforming a hexagon by altering >the lengths of its struts, so that all together, they form a sphere: I've used "hexagons" and "pentagons" to summarize groups of 5 and 6 triangles respectively. The geodesic construct I'm looking at has only pentagonal and hexagonal arrangements of triangles (hence the "spokes" and "rim" nomenclature). But really the construct is all triangles. The big sector triangles (of which there are 20) are subdivided into smaller ones. What I'm imagining is that these "hexagons" (each composed of 6 triangles), if removed from the construct and stacked like a tower of slightly convex quarters, would not prove to be identical. They would all be slight distortions of the pure equilateral triangle. But given a very large number of such, and the very eency weency bit of degree each would contribute to the missing 720 by virtue of its deviance from pure equiangular 60-60-60, I am supposing that even the naked eye might have trouble distinguishing these guys from equilateral triangles -- but the wouldn't be! Bucky has a disagreement with Calculus which [at least he supposes] says that if you draw a polygon of diameter epsilon around point x on the surface of a sphere, and draw spokes out to its n corners, and add the central angles so defined to get D degrees, that D can be made to approach arbitrarily close to 360 as epsilon->0. Bucky has a problem with this: precisely that the 720 "missing" degrees, distributed evenly to all points x, is irreducible. No matter how small the radius of the surrounding polygon, point x is _got_ to contribute a finite positive number of degrees to the total 720. A sphere is therefore *not* ideally locally flat. The super high frequency omnitriangulated construct I'm imagining is an alternative "skeletal" sphere, where the vertices are _defined_ to have the requisite missing degrees, and all vertices are missing the same amount of degrees. I'll stop repeating myself now. Sorry all. >I have a geodesic sphere model composed of 20 hexagons and 12 pentagons. >(The manufacturer neglected to specify exactly what kind of construct >it was, but I've assumed it to be an icosa-sphere.) Around this model >I count 92 vertices. This means that each vertex must be 720/92=7.826 >degrees less than 360. So, in general, the algorithm need only search >through strut lengths which result in hexagons whose central vertex is >352.174 degrees. Yes, you're thinking along similar lines. But as Chris posted, if you actually measured the degrees around each of your vertices, you will probably find that they do NOT each contain the same number of degrees less than 360. Rather, some will have fewer and some more degrees. I suspect this cuts down dramatically on the number of edge lengths required for construction. Your construct will, of course, have exactly 720 degrees less than 360*92 vertices. That is true for any concave/convex (uncored) polyhedron. Alternatively, I am proposing a different strategy which _insists_ on this equality in surrounding degrees. Apparently, this is _not_ consistent with the Class I geodesic algorithm, which is the most familiar. Oops, I did it again. >This will cause the hexagon to form a shallow, hexagonal pyramid, >whose apex is aproximately 25 degrees. The more hexagons, the shallower the local apex. I perfectly flat hexagon is approached, but never reached. ------------------------------------------------ Kirby T. Urner pdx4d@teleport.com 4D Solutions (teleport.com is a public access node) ========================================================================= Date: Fri, 2 Sep 1994 21:14:01 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: Geosphere & sci.math I was intrigued by Kevin's post-through of sci.math postings dealing with dispersions of points on spheres: how to maximize the total interdistance, make the distances have the lowest standard deviation or whatever. Continuing this thread of an imaginary geosphere defined to have exactly the same number of degrees around each vertex (summing surface angles), I am led to wonder whether this optimization would be congruent with some other optimization e.g. maximizing interdistance of a given point group. It would seem that my algorithm is about "evening out curvature" as much as possible, which intuitively seems also to mean making each point as far from its neighbors as possible (i.e. to make the spokes out to them as spread out as possible, as close to 360 as possible -- for all vertices). What I'm wanting now is to construct a low frequency version of such a creature, and I'm feeling a bit at a loss for numerical recipes. I think I'll go off and scratch my head for awhile, #:-I <-- furrowed brow emoticon. maybe check out some spherical geometry texts in my copious free time. :-) ------------------------------------------------ Kirby T. Urner pdx4d@teleport.com 4D Solutions (teleport.com is a public access node) ========================================================================= Date: Fri, 2 Sep 1994 21:19:51 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: Non-synergetics >In Article <199409020503.WAA13807@teleport.com> >Kirby Urner writes: >>>Geoffrey Wherrett (wherrett@mech.ubc.ca) wrote: >>> >>>: In article , smtc5@uoft02.utoledo.edu >>>: >Why does water drain counter-clockwise? >>> >>>Only in THEORY, really. The Coriolis effect is quite negligible compared >>>to other probable effects (geometry of the draining vessel, initial >>>movement of the water, etc.) I think winds and such larger systems DO >>>show the effect, but will leave that as an excercise for the reader ;-) >> >>I just came back from southern Africa. My wife shouted for me >>to come into the kitchen to see how the water was draining in >>the other direction. Certainly seemed empirically convincing. >>Everyone check your kitchen sinks and bathtubs, lets see if >>we all go around in the same direction. No stirring with hands >>allowed. > >I tested it. It always drains counter-clockwise even if swished >around the opposite direction with your hands (it switches part >way through.) > Steve Mather > > I concur, counter-clockwise. Now I'm going to send an email to dad in Lesotho (surrounded by South Africa) asking him to double check his sink. I'll post his reply. ------------------------------------------------ Kirby T. Urner pdx4d@teleport.com 4D Solutions (teleport.com is a public access node) ========================================================================= Date: Sat, 3 Sep 1994 19:24:33 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "Robert L. Read" Organization: CS Dept, University of Texas at Austin Subject: FElt can't do prestressing of cables Jason Gobat, a coauthor of FElt, sent this reply in response to the question of pre-stressing that was posted here I while ago. >From jgobat@MIT.EDU Fri Sep 2 16:03:36 1994 Robert - I don't know of an obvious way to make FElt solve a cable problem. The easiest thing that I can think would only work if you knew the shape of the hanging cable beforehand. If you had this, you could model it as a series of truss elements and lump the self-weight of the elements as vertical point loads at the nodes. The tension in each element would then be a rough approximation of the tension in a given portion of the cable and the support reactions should also be reasonable approximations. I'll be the first to concede, however, that this really isn't all that easy - figuring the shape is often a large part of the problem you want to solve to begin with and modelling a self-weight load as a series of point loads is usually not much fun. Sorry I couldn't be more help. You might want to suggest that he try to find a piece of software that was designed specifically for cable problems. I'd think that something of the sort must exist somewhere ... Jason -- Robert L. Read, Member of the League for Programming Freedom ========================================================================= Date: Sat, 3 Sep 1994 21:51:49 EDT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Hawku@AOL.COM Subject: Quadrants I am interested in substituting quadrants for straight lines in various polyhedra. I have found that 6 quadrants can be substituted for a hexagonal continuum (as in cuboctahedron), 4 can substitute for a square continuum (as in octahedron ); and they can combine to form the irregular tetrakaidecahedron (8 hexagonal & 6 square openings). Quadrant-based polyhedra should facilitate motion in mechanical design because of their curvature. In the quadrant-based cuboctahedron (curVE) all quadrants lie on the surface of a sphere which would circumscribe a regular cuboctahedron (vector equilibrium). Every point along a quadrant is equidistant from the center. In the cuboctahedron only the vertices are equidistant. A straight-line radius from the center of a quadrant-based cuboctahedron with it's pivot at the center can rotate to any position on the circumference. ========================================================================= Date: Mon, 5 Sep 1994 05:24:50 MDT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "Ken G. Brown" Organization: BEST Online Subject: Re: Geosphere & sci.math >Fri, 2 Sep 1994 21:14:01 -0700 >Kirby T. Urner pdx4d@teleport.com >4D Solutions (teleport.com is a public access node) >I was intrigued by Kevin's post-through of sci.math >postings dealing with dispersions of points on spheres: >how to maximize the total interdistance, make the >distances have the lowest standard deviation or whatever. A paper that I came across several years ago seems to relate directly to the discussions here. The paper appeared in the published papers from the Third International Conference on Space Structures. Published by Elsevier Applied Science Publishers (London or New York). Title: Structural Configurations from Geometric Potential. Author: J.W.Butterworth, Senior Lecturer, Dept. of Civil Engineering, Univ. of Auckland, N.Z. Abstract: A potential function is defined for a set of nodes lying on a surface. Then moving the nodes about on the surface until the potential is a minimum results in node positions which may be interconnected to create configurations of optimum regularity. The concept is illustrated using a spherical surface but may be applied to more complex surfaces. -Ken- (kbrown@atc.edmonton.ab.ca) ========================================================================= Date: Mon, 5 Sep 1994 19:22:06 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Bob Hiltner Organization: Eskimo North (206) For-Ever Subject: Re: Non-synergetics Kirby Urner (pdx4d@TELEPORT.COM) wrote: : I just came back from southern Africa. My wife shouted for me : to come into the kitchen to see how the water was draining in : the other direction. Certainly seemed empirically convincing. : Everyone check your kitchen sinks and bathtubs, lets see if : we all go around in the same direction. No stirring with hands : allowed. : ------------------------------------------------ : Kirby T. Urner pdx4d@teleport.com : 4D Solutions (teleport.com is a public access node) Well, in the name of anecdotal evidence!! :-) Double sink, both sides drained clockwise in Seattle. (still think this has more to do with geometry of the sink and drain than the rotation of the earth over the 3 seconds of draining... -- Bob Hiltner "It is not enough to do well (and I hope you do), you must also do good" ^^^^ ========================================================================= Date: Mon, 5 Sep 1994 14:45:00 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: smtc5@UOFT02.UTOLEDO.EDU Organization: University of Toledo Subject: Re: Geodesic sphere algorithm Following this discussion, I struck upon an idea. Since we're working, in essence, backwards from normal geodesic calculations, I hit upon the idea that perhaps we don't need pentagons in our geodesic sphere. Now maybe it has been too long since I've thumbed through Synergetics, but if we were it simply subtract those 720 degrees from a hexagon tiled plane, without the restraints of subtracting the additional 12 triangles, perhaps we could create a sphere tiled entirely with 6 triangles at each vertex. All other rules could apply. I know ther's something fundamentally wrong with that idea, or so it seems. Someone help me out here. =0 Steve Mather ========================================================================= Date: Wed, 7 Sep 1994 08:19:07 -0400 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: John Brien unsubscrube ========================================================================= Date: Wed, 7 Sep 1994 23:29:46 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: Geodesic sphere algorithm >Following this discussion, I struck upon an idea. >Since we're working, in essence, backwards from >normal geodesic calculations, I hit upon the idea >that perhaps we don't need pentagons in our geodesic >sphere. Now maybe it has been too long since I've >thumbed through Synergetics, but if we were it simply >subtract those 720 degrees from a hexagon tiled plane, >without the restraints of subtracting the additional >12 triangles, perhaps we could create a sphere tiled >entirely with 6 triangles at each vertex. > >All other rules could apply. > >I know ther's something fundamentally wrong with that >idea, or so it seems. Someone help me out here. =0 > > Steve Mather > Steve -- A tempting thought, and well worth proposing. Yet, as you suspect, you are tempted by an impossibility -- something maybe an MC Escher type could nevertheless depict. Accepting Euler's Law (V+F=E+2) as given, one can prove that 12 pentagons are required (no more, no less). First, assuming all hexagons: where v = number of vertices... if you count out 6 spokes stemming from each vertex, you'll end up counting every edge twice (because of a vertex on each end), so e = 6v/2 or 3v and the number of faces times 3 will give twice the actual edge count, since each edge has a face on each side, so 3f=2e or f=2e/3 or 2v Ergo, since (Euler) v+f=e+2, v+2v=3v+2 or 3v=3v+2 which is impossible. Second, assuming h vertices at the centers of hexagons and p vertices at the center of pentagons... if you count out 6 spokes for each of the h vertices and 5 for each of the p, you'll get twice the number of edges again, so e=(6h+5p)/2 and f will again be 2e/3 or (6h+5p)/3 Since the total number of vertices is p+h, it follows that (p+h)+(6h+5p)/3=2+(6h+5p)/2 (Euler's Law) This simplifies to simply p=12. Q.E.D. Note that we've proved nothing about the relative positions of the pentagons. In fact, they *don't* have to appear only at the 12 corners of a spherical icosahedron, hence the endless permutations of possible buckyballs when larger numbers of carbon atoms are involved. Given the stresses involved, at lower numbers of atoms at least, it seems the molecules are stable if the pentagons are as far apart as possible, as in C60 (fullerenes being the same as our omnitriangulated buckyballs, with the spokes inside the hexagons and pentagons removed). ------------------------------------------------ Kirby T. Urner pdx4d@teleport.com 4D Solutions (teleport.com is a public access node) ========================================================================= Date: Thu, 8 Sep 1994 02:31:06 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Design Science Revolutionary Essay 1 Design Science Revolution How to Implement It? PART ONE by Kirby Urner Central to the Design Science Revolution (DSR) is the concept that humans earn the right to eat through jobs, that basic survival is a reward to be denied those who are unable, for whatever reason, to deal themselves in to the global cash economy. The idea that humans without so much as a pair of boots should nevertheless be "self booting" (pull yourself up by your bootstraps) is fallacious. Lots of situations place humans at such a disadvantage that recovery without externally provided life support is impossible. Cases range from the starving African in a war-torn land to a heart patient in urgent need of triple bypass surgery. Left purely to his or her own devices, said human will die. To construct a global economy that provides basic survival as a basic entitlement means overhauling the economic picture to some degree. Economists are forever speaking of the need for competition to bring honesty and integrity to the market place. Monopolies suck. And yet the discipline of economics itself goes largely unchallenged by any competing discipline. Rather than struggle within current economic jargons to erect a conceptual apparatus that would lead us toward providing a supportive infrastructure for humans without hope, the DSR might choose to implement a parallel discipline in direct competition with Economics. Although General Systems Theory (GST) has not traditionally been posed as a competitor, it has the necessary elements: a big picture scope, a focus on models with large numbers of variables and interrelationships, and a partial overlap Fuller's key contributions to our DSR syllabus. Synergetics and GST have a lot to provide one another. GST will posit the solar fusion furnace as the principal corporate (in the sense of "stellar body") sponsor of all energy-driven systems on its planet. Earth is similar to a nonprofit entity: it survives on grants (not loans -- the sun is not lending but sending). Human systems are basically analogous to water wheels or wind mills -- circuitry designed to serve humanly conceived ends is driven by paddles inserted into the entropic downward flow of solar energy. The human designs tend to ephemeralize (involve less physical resources, more intellectual ones) as know-how increases. This syntropy in the know-how domain, combined with the sun-stream of energy ever flowing to the planet, is what gives us successive generations of basic operating system. GST borrows a lot from engineering: operating system in place of "economic system." And lets remember the OSs come in many flavors. We're not talking "capitalism" vs "communism" or "free market" vs "command economy." We're talking programmable circuitry, routines, business rules. Programming our systems to deliver enough sun-energy to each human to permit basic survival is Challenge Number One. GST says we have the know-how to do it, if the economists would just take a back seat and let us do the driving for a change. Hyperlinks: GST Dymaxion Map Global Resources World Game Scenarios ------------------------------------------------ Kirby T. Urner pdx4d@teleport.com 4D Solutions (teleport.com is a public access node) ========================================================================= Date: Thu, 8 Sep 1994 02:33:30 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Design Science 2 Design Science Revolution How to Implement It? PART TWO by Kirby Urner How does General Systems Theory model the human life support system? The system is sun-driven. Humans insert their "water wheels" into the energy flow to drive their programmable circuits. The machinery is repetitive, cyclic, but changes slowly. Ships carry cargo from point A to B to C back to A and repeat. Commercial airliners repeat their to and froing daily, weekly, schedules subject to change, routes coming and going. The daily grind is global. Hypermedia provide the most changeable aspect of the system. Ships and planes are big and heavy assets with lots of momentum, like "heavy stones." But "talk is cheap" (some say), meaning dreams are free. Where we brainstorm the future is in our imaginations. But the imagination is not some isolated theater. The imagination is hypermedia -- multimedia linked every which way to create the circuits our thoughts travel around (again, somewhat repetitively). When we think about changing the big patterns with lots of momentum attached, we start with our hypermedia, advertising our alternative futures, selling sponsors on this or that path towards fun and profit. We do this individually, and at the community level through Hollywood, mass media and politics. The site (or seat) of intelligence, where the links between all the media are made and saved, is the individual. GST models individuals in terms of Personal Workspaces. Not that everyone on the planet has a multimedia workstation of the hardware variety, complete with telecommunications. Far from it. But each individual imports vast quantities of information, repackages it, edits it, recombines it, links it up in uniquely individual fashion (with lots of commonalities, even banalities mixed in) and puts it out their. We each "inload" and "outload" as poet Gene Fowler puts it. The Personal Workspace is a site for importing energy/information, modulating and recombining it, and sending it back out onto the circuits. The global network of PWSs modulates the big energy flows with its hypermedia imaginations. Thoughts precede deeds. Dreams precede actions. You and I take in, do our magic, and put it out. All of us doing that together create culture, which in turn consists of story lines. We enact stories. The metaphor here is the Globe Theater (all the world is a stage) and World Game (the men and women are the players). Thank you Will! The storyline we're currently enacting is a Great Tragedy. Humans are too screwed up to save their friends from catastrophe, and soon, maybe, we'll all be in a desparate plight. Resources are insufficient and population is spiraling out of control. That's the story. Hypermedia have the power to provide persuasive alternatives. Hope of raising global living standards, of empowering women to escape child bearing as their one and only worthy career, of empowering men and women to find engineering a humane discipline phasing into Art-Science on the one hand, and Revolutionary Design Science on the other, is in the hypercards. Time to shuffle and deal. Time to write some now cue cards, to reprogram the teleprompter. It doesn't have to be a Great Tragedy. Unemployed Defense Workers of America Unite! Build us some dymaxion dwelling machines, air-deliverable if you please. We'll reprogram our sun-driven circuits to bring you the latest in Sun Microsystems workstations in exchange (plus you get to live in your design creations -- and of course we'll keep the old Victorians and brownstones around. Some of the ticky tacky junky houses we could explode on television, after providing their tenants with fancy upgrades of course...) ------------------------------------------------ Kirby T. Urner pdx4d@teleport.com 4D Solutions (teleport.com is a public access node) ========================================================================= Date: Thu, 8 Sep 1994 03:16:24 -0700 Reply-To: bb297@scn.org Sender: List for the discussion of Buckminster Fuller's works From: John Braley Subject: Non-synergetics Another lurker surfaces! Actually, aside from a weekend at the Synergetics Conference some summers ago at the UCLA campus (where I met several of the people attached to the names I see in this forum), I've been not just a lurker with regard to GEODESIC but in the larger BuckyWorld as well. Well....now to start spinning. Coriolis force "In 1889, Ferrel summarised the effect of the Coriolis force quite succinctly when he stated: 'if a body moves in any direction upon the earth's surface, there is a deflecting force arising from the earth's rotation which deflects it to the right in the northern hemisphere and to the left in the southern hemisphere.' This 'deflecting force arising from the earth's rotation' may be considered to be a consequence of moving objects, such as masses of air conserving their angular momentum with respect to the surface of the earth, which is itself rotating. Bodies moving over the surface of the earth on straight-line paths are apparently deflected to the right of their line of motion in the northern hemisphere. There must be a force that generates the deflection. This apparent force is known as the Coriolis force, after the nineteenth-century Greek mathematician Coriolis who formulated the idea. The Coriolis force (perhaps better called the Coriolis effect) is an apparent force which needs to be introduced into any analysis of motion on a rotating frame of reference such as the earth to explain the apparent deflections of straight-line trajectories. This apparent deflecting force will act on all bodies moving over the surface of the earth, and unless compensated will cause them to curve continuously to the right in the northern hemisphere and to the left in the southern hemisphere. Normally only the horizontal component of this force is considered; it always acts at right-angles to the direction of motion of the body. It cannot change the speed of movement, only its direction of motion." -- from _Weather Systems_ by Leslie Musk. When I was a small child my grandmother told me about an article (probably in Reader's Digest) that said water always spiralled down the drain in the same direction (in the Northern Hemisphere). We had a lot of fun exploring this after my baths. Many years later I came across an article by someone who explored this question with the resources of a hydrology lab. He said that even though they filled their tub very carefully and waited many hours the residual currents in the water were still detectable by their equipment. Upon draining, they got 50/50 on handedness of the rotation of the vortex. (Also they noticed that the vortex always reversed its direction for the last of the outflow.) John C. Salzsieder, Phillips University, wrote (in part) in the February 1994 "Physics Teacher" under the title "Exposing the Bathtub Coriolis Myth": "It is a common misconception that water spirals down a bathtub drain clockwise in one hemisphere (northern or southern) and counterclockwise in the other. Many students have heard this story and relate it to the rotation of low pressure and high pressure weather systems. The Coriolis force on water in a bathtub, however, is much too small to be observed. What really causes water to spiral down a drain is the residual momentum of the water. The water in a sink or a bathtub will almost always have some net angular momentum in one direction or the other. This can be easily demonstrated, and the bathtub Coriolis myth can be dramatically debunked." Salzsieder goes on to describe a classroom demonstration involving two sinks filled with water, stirred clockwise in one and counterclockwise in the other. 15 minutes after the stirring the water appears motionless but still has sufficient residual motion to drain in the directions stirred. In the middle of a pole-to-pole TV travel documentary, Michael Palin, with other tourists, visited a demonstration of the Coriolis effect at the equator. A gentleman standing a few yards to one side of the "official equator" line drained a plastic tub, pointing out the direction of rotation of the vortex (easily seen with the help of small corks). Then he stepped a few yards past the equator to the other hemisphere and again drained, this time pointing out the opposite handedness of the vortex. The awed tourists rewarded him. I, too, might have made a small contribution -- based on Performance Art chutzpah. Even in large scale weather systems the Coriolis effect competes with other factors such as pressure gradients and friction in determining chirality of rotation. On the scale of the few inches involved in a sink or a tub the Coriolis effect must be sensationally small and easily dominated by factors such as residual currents and shape of the container (and drain). This was expressed quite reasonably by Bob Hiltner, in the 3rd response to the original question. (Parenthetical paragraph: If I were to accept the Coriolis/drain thesis wouldn't I expect a clockwise vortex in the Northern Hemisphere?) -- John Braley bb297@scn.org ========================================================================= Date: Thu, 8 Sep 1994 18:18:15 GMT Reply-To: wherrett@mech.ubc.ca Sender: List for the discussion of Buckminster Fuller's works From: Geoffrey Wherrett Organization: Department of Mechanical Engineering, UBC Subject: Re: Non-synergetics It has been a lot of fun to see my explanation for the direction of draining debunked so effectively. If you want to get to the bottom of a scientific question this seems to to be the place to go. Geoff Wherrett ========================================================================= Date: Sat, 10 Sep 1994 08:27:23 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Lee Wood Subject: hibernating My current workload is forcing me to unSubscribe from all the interesting lists to which I subscribe. So, if you don't hear from me for a few months, I'll be snowed under and hibernating. see you in the early spring. =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= Lee Wood | Lee_Wood@sfu.ca | INTJ spoken here. =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= ========================================================================= Date: Sat, 10 Sep 1994 19:32:23 -0400 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "" Subject: Re: Geodesic sphere algorithm >Following this discussion, I struck upon an idea. >Since we're working, in essence, backwards from >normal geodesic calculations, I hit upon the idea >that perhaps we don't need pentagons in our geodesic >sphere. Now maybe it has been too long since I've >thumbed through Synergetics, but if we were it simply >subtract those 720 degrees from a hexagon tiled plane, >without the restraints of subtracting the additional >12 triangles, perhaps we could create a sphere tiled >entirely with 6 triangles at each vertex. > >All other rules could apply. > >I know ther's something fundamentally wrong with that >idea, or so it seems. Someone help me out here. =0 > > Steve Mather > Hmmm. Is there a polyvertexiated configuration in which always and only six edges meet at each vertex? Just asking... not making an assertion. Nothing regular (equiangular, equilateral) comes to mind. --------------------------------------------------------------------------- Mitch C. Amiano amiano@delphi.com ========================================================================= Date: Sat, 10 Sep 1994 19:32:37 -0400 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "" Subject: Re: Design Science Revolutionary Essay 1 ... >to the market place. Monopolies suck. And yet the ... The problem with revolutions is that they have a strong tendencies to leave many problems unsolved while at the same time facilitating the installation of a censurious - if not dictatorial - leadership. It is also a notable, if obvious, trend that students will eventually diverge (improve, alter, redefine) from a teachers' instructions given sufficient time. This hints at dangers in attempting to reinvent society... revolutionaries tend to polarize their thoughts until non-members are vilified. Fuller recognized this tendancy even in himself, and corrects himself in his own writings, as in this excerpt from "Guinea Pig B": ...They and their only-selfishly-motivated masters are gambling the future of all humanity to win only the continuing increase of their personal economic power control for the few remaining years of only their own lives. ... ... On rereading what I have just said about humans falsiying critical information, I am retrospectively shocked at my making those two negative citations. ------------------------------------------------------------------------- Mitch C. Amiano amiano@delphi.com ========================================================================= Date: Sat, 10 Sep 1994 18:42:28 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: Design Science Revolutionary Essay 1 > >The problem with revolutions is that they have a strong tendencies >to leave many problems unsolved while at the same time facilitating >the installation of a censurious - if not dictatorial - leadership. > Revolutions per se have a bad reputation in the US, partly because of its censurious - if not dictatorial - mass culture. One book I read attributes this to USAers never having a real revolution in their history, only a war of independence (same elite, just wanting to not pay taxes across the ocean). In any case, I agree that the Design Science Revolution will get nowhere as a propaganda war, despite my rousing little essays. Fuller's idea, to which I also subscribe, is that artifacts, not political ideologies, make the big difference. The media shows I've been advocating, science fiction based on props from the near future (attainable, not Star Trek or the Jetsons), would give corporate America a chance to advertise postindustrial consumer goodies in the traditional logo-language of commercial television. As long as we don't disrupt the superbowl look and feel, no sense of "revolution" will disrupt the Design Science program. Just more people will decide to live in a house with the latest in design science artifacts from General Dynamics or whatever. More computer screens will have the dymaxion map of the world option displayed. Not a revolution of too many slogans and billboards, although bumper stickers always have their place. ------------------------------------------------ Kirby T. Urner pdx4d@teleport.com 4D Solutions (teleport.com = public access node) Portland (PDX), Oregon "All realities are virtual" -- KU ========================================================================= Date: Sun, 11 Sep 1994 22:20:00 AST Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Victor Huerfano <960912813%RUMAC@UPR1.UPR.CLU.EDU> Subject: Re: hibernating Good lock.. ========================================================================= Date: Wed, 14 Sep 1994 16:11:11 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Mark Stowe Subject: 'revolutionary' discussion groups >> >>The problem with revolutions is that they have a strong tendencies >>to leave many problems unsolved while at the same time facilitating >>the installation of a censurious - if not dictatorial - leadership. >> As much as I like most of the political commentary here I am really looking for a list or lists where folks are batting around very specific ideas about exactly how future egalitarian ecotopian Fulleresque on-line communities might work. Any one have any suggestions? Mark --------------------------------------------------------------------------- Mark Stowe c/o Jon Reiskind Department of Zoology University of Florida Gainesville, FL 32611 USA E-mail: MKS@ZOO.UFL.EDU phone: 904 373 3202, 904 392 1187 fax: 904 392 3704 ========================================================================= Date: Thu, 15 Sep 1994 01:46:18 EDT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Chris Fearnley Subject: SUMMARY: Computer Graphics and Mathematics Tools for Synergetics and Domes SUMMARY: Computer Graphics and Mathematics Tools for Synergetics and Domes Throughout the history of list Geodesic, people have posted requests for software tools to help build domes and solve other Fuller-related geometry and architecture modeling problems. In the FAQ I have started collecting citations to extant mathematics and graphics packages that may be useful to people working on such projects. [See below (Appendix) for the current summary of this compilation.] But what we really need is a comprehensive tool or perhaps a toolbox of synergetically intercomplementary tools for working on problems from a synergetics perspective - something that would allow one to model domes, tensegrities, the isotropic vector matrix, and etc., very easily. In April I posted a message asking about such tools. The result was a long thread about the prospects for writing such a tool from scratch which I will attempt to summarize now. Nevertheless, work has not yet started on this project. If volunteers come forward, perhaps we can begin designing the program more concretely. In my original message I suggested looking at the platform independent approach provided by X Windows and C programming (PEXlib, in particular). The main problems with this approach are that it locks us into a particular windowing system (with its overhead) and not everyone has X on their system (in spite of the fact that X is free - just like the air - and monocrome X servers have been written for those who don't have color displays). One problem is how to model synergetics on a computer? Since almost all the known algorithms for computer graphics and mathematics are based either on calculus or XYZ coordinates or both (very non-synergetic), how can we write a program that will ``feel'' intuitive like synergetics. The simplest approach would be to use the non-synergetic (ick!) computer tools that are available. Similar to the synergetics constant approach Fuller discusses in _Synergetics_, we could translate the synergetic point of view into traditional functions. To the end user it would appear that everything is in 60-degree coordination. Only the low-level functions would need to deal with the XYZ-coordinate system. The question still remains: ``Is it possible develop a computer graphics/mathematics system from scratch based on the synergetics fundamentals of space, event, vector, and etc., and have it appear on an A pixels by B pixels screen?'' Or ``Should we use the XYZ-based graphics libraries (functions, etc.,) that already exist?'' Until the first question is answered in the affirmative, it would seem that the second approach would be more prudent (building on the tools of others). A Scenario: The synergetics computer modeling tool from the point of view of PEXlib. PEXlib is a library of 3-D graphics functions for use with the high-quality, highly flexible, network-transparent, graphical windowing system, X. We could write PEXlib functions that would perform several synergetics tasks: [Thanks to Kirby Urner, Ben Discoe and Kurt Przybilla for their ideas which I have incorporated into this list.] - Draw a polyhedron (regular, irregular, # of vertices, faces, edges) - Draw a Tetra, Ocata, Icosa, etc,. of the given edge length - Show other perspectives of the model - Rotate the model x degrees about this axis (along this great circle) - Draw sets of great circles of symmetry for the structure - Explode the structure into its component A, B, T quanta modules - Summarize the topological abundances, number of quanta modules, surface and central angle measurements, solid angles, tetra-volume and any other quantifiable information about the structure - Pulsate the Vector Equilibrium (show the animation) - Place the structure in an Isotropic Vector Matrix Field - Show the dual of the given structure - Unfold the polyhedron into its "map" - Change vectors to arc (and visa versa) to show spherical concepts - Show a structure of the given frequency (increase, decrease frequency) - use frequency to reflect scaling - Give the structure properties of molecular chemistry (fullerene modeling) - Model interferences of events and vectors - Make vertices spheres or "events" - Mode for using the octet truss to define structures - Inside-out the given structure - Analyze the stability of the shape, model, structure Below are some quotes from the thread where we last discussed these issues. Mitch C. Amiano introduced the need for a form language to deal with synergetics more easily: ==================== Begin Mitch's contribution ==================== >From the number of 3D CAD packages I've explored (some in depth, some only briefly), none appear to be very useful when attempting to model triangulated polyhedrals. I think the general problem is language - a form language to be exact. The geometric vocabulary of PC based 3D CAD systems is stilted, lacking in some very basic nouns/objects (forms) and verbs (manipulative operations). I suppose what I'm trying to say is that the problem you are discussing may have a solution to be found in the solution to a more general case problem: modeling and manipulating geometric forms (not just IVM's/geodesics). My ideal for such a modeling tool would implement the "form language" developed by Robert Williams in his 1979 book _The Geometrical Foundation of Natural Structure: A Source Book of Design_ (Dover Press). Ok, I'm quoting from the book, as a teaser: "Polygons and polyhedra can be generated or have identity changes through ten principal methods: 1. Vertex Motion 2. Fold 3. Reciprocation 4. Truncation 5. Rotation-Truncation 6. Augmentation-Deletion 7. Fistulation 8. Distortion 9. Dissection 10. Symmetry Integration" The[se] samples could be viewed as operators in a language in which the objects were geometric shapes (eg polyvertexia). Of course, the list is incomplete, and a method of specifying only an addressing mode (prepositional phrase?... ie "stellate only this half of this polyvertexia") is missing. But at the notational level there is also his {edges-at-a-face , faces-at-a-vertex} syntax for specifying polyhedra ( ie {3,5} == icosahedra, {3,3} == tetrahedra, {4,4} == octahedra ) I think it is a 'disciplined' approach, as opposed to a 'rigorous' approach. Williams admitted to its incompleteness, but that is unavoidable. ==================== End Mitch's contribution ==================== Ben Discoe made the following report on his work in this area: ``I think I should mention my work here. I have a 3d modeller project which I've been working on for a few years; initially it was to explore polyhedral geometry (since I was studying _Synergetics_ and getting frustrated with paper models) but I'm afraid it's evolved into a easy-to-use "normal" 3D modeling program over the years. It does do Bucky-style "frequency" tesselation and can find the dual of any shape you give it. I wrote it to be portable, versions exist for Amiga, MSWindows and Mac, but the non-Amiga versions need a little work. It's written for portability, so any new platform you might suggest (say, Linux w/X) should be a quick port, given I have access to a machine capable. The modeller is called "PolyWog", and it's currently freeware (I'm a "revolutionary" too :-) I'm considering copylefting it.'' Kirby Urner's posts don't lend themselves to easy editing so here is one of his messages in full: ==================== Begin Kirby's contribution ==================== MORE THOUGHTS SYNERGETICS GRAPHICS (inspired to recent postings brainstorming software/hardware issues)... How would 4D synergetics differ at all from standard 3D graphics? Hardware is uniformly XY-coordinated when it comes to placing pixels on the screen. The existing library of 3D drawing tools is also XYZ of course. No need to reinvent the wheel first off. Starting from the whole and some of the parts would be the most faithful beginning. We should assume that the entire isotropic vector matrix (IVM) is invisibly present and brainstorm primitive function calls that would take advantage of this infrastructure. E.g. one should be able to place an A or B module (translucent or opaque in higher-end apps) with a minimum of fuss. Grabbing A and B mods with the mouse and dragging, with subsequent controls to adjust size and orientation might be an option. In general, the IVM is most conveniently traversed by jumping in a direction indicated by one of the tetrahedron's 6 edges. Putting these 6 vectors tail-to-tail and producing their 6 negative counterparts pointing at 180 degrees produces the 12-spoked hub of the vector equilibrium. Perhaps 2 sets of complementary zig-zags, i,j,k and l,m,n -- which together outline a tetrahedron -- would be useful primitives in an interpreted synergetics programming language. The polyhedra of the synergetics hierarchy would all be primitives and the synergetics hierarchy would somehow comprise the infrastructure for most function calls. E.g. the default icosa would have a pre-defined relationship to the default tetra. Each polyhedron would have internally defined methods for breaking up into submodules, changing its chordal frequency, outputting its volume (a number) in tetravolumes etc. A library of primitive objects each with a set of internally defined powers would seem the way to go. One might invent a layer of synergetics notation, a programming language, that underlying XYZ routines would interpret. For example, one can label the centers of spheres in a closest packing with integers, given a set of basis vectors that point along three edges of a rhombohedron -- a slanted cube. A matrix converts [23,-5,-10] (some sphere) to its corresponding Cartesian floating point coordinates. I once derived these matrices and programmed a very primitive Logo-like turtle to jump from sphere to sphere in synerspace (used SmallTalk on a 286). Just off the top of my head, an interpreted synergetics scenario (storyboarding) language might look something like: place Amod size .5 at origin as "A1" place Bmod bondedto F1 of A1 as "B1" copy A1 to (origin+2*j+3*i) as "A2" rotate A2 axis E1F1 by 90 show A1 color red mode opaque show B1 color blue mode translucent show A2 color red mode opaque OR (another variation of the same thing) A1=PLACE(Amod,0.5,origin) B1=FBOND(Bmod,A1,F1) A2=COPY(A1,origin+2j+3i) A2=ROTATE(A2,E1F1,90) =DRAW(A1,red,1) =DRAW(B1,blue,0) =DRAW(A2,red,1) Ultimately, what we're aiming for is a higher level scenarios language that might allow us to write something like: begin scenario("syn1") explode coupler into mods slowly zoomin any Amod and unfold to planenet slowly display planenet with dimensions for 10 seconds foldup planenet and illuminate Amod within tetrahedron quickly print Amod volume as fraction of tetrahedron end save "syn1" to archives upload "syn1" to internet(addr:GEODESIC) ==================== End Kirby's contribution ==================== Kevin Sahr posted a very nice message giving his thoughts on designing a synergetics modeling package. I like his ideas (except I'm not ready for C++ programming yet :) and include them here: ==================== Begin Kevin's contribution ==================== I too would very much like to see software like this developed, and by the end of this summer I think I could also volunteer some time towards making this a reality. I've been a professional programmer for the last 5 years, with a significant chunk of that time spent doing high-end 3D graphics work. For what it's worth, here's my slant on what I've seen of the discussion so far. First, though the choice of an initial platform and graphics library is obviously important, I think the real key to doing this right is to use something like the SmallTalk model-view-controller paradigm. Specifically, I think we should develop a display-independent back-end, that consists of a set of data structures and a command language that drives their manipulation that contains no platform/library-specific graphics commands in and of itself. While it's got it's problems, I think the obvious best choice of a language to do this in is C++. Next we define an abstract display class, where any specific instance of this class would have to define some canonical set of drawing methods. One of the first display classes to create would be a text one: i.e., to draw a polygon to it would simply print-out the vertices of the polygon or whatever. We also define an abstract controller class, which would issue some set of commands to manipulate the data structures. Again, the first obvious controller to define would be a text-based one, where you type in what you want to happen. If this was well-designed, then different people could code specific display classes for their favorite platform/graphics library. And if the models were always internally manipulated by some platform-independent command/function set, then GUI's for different platforms could be layered on top of that command set. Unfortunately we're stuck with XYZ graphics libraries, at least at some level (since the pixels on our monitors are in rectilinear coordinates; always struck me as an obvious idea to make monitors with a hexagonal grid of pixels rather than rectilinear. Seems like it should give a better display [with less aliasing, etc.] for the same number of pixels). But there's no reason why our internal manipulations can't be IVM based; indeed, I think that the development of such a graphics language would be highly educational. As to which graphics library to implement in first, I personally think that the best 3D graphics library by far is OpenGL. As far as I can tell the only reason people use anything other than GL for 3D graphics is because, until very recently, GL was a proprietary standard that was only available on SGI machines (which were, again until very recently, very expensive). Now that OpenGL is being ported to many other platforms I personally think it's going to kill all of it's competition (which consists, as far as I can tell, of PEX, PHIGS, and StarBase (:-()). Also, I believe there are PD GL work-alikes available for both the PC and the Mac (called VOGL, I believe). But again, it really doesn't matter to me which display someone works on first; because if this is done in the manner I suggest the display, while obviously important, is not where the meat of this project is. Give me a set of vertices for a polyhedron and in GL I can draw it on the screen shaded, lighted, and with your mother-in-law's face texture-mapped onto it with no trouble. With a (very) little more trouble I could draw it on a Mac (at least as a wireframe, sans your mother-in-law's face :-)). Believe me, I'm not trying to trivialize the graphics portion of this project (and I'm _especially_ not trying to trivialize the mouse-based user interface portion of such a project!). But given that we've got a variety of platforms here I think we could get the biggest bang for our time by not cutting any of them out of the action from the get-go. ==================== End Kevin's contribution ==================== Kirby responded: ==================== Begin Kirby's response ==================== I enjoyed your manifesto advocating a C++ engine over which various developers could pitch their interface tents (how's that for mixing metaphors?). Using the OOPs model, I'd suggest that any polyhedron object be prepared to answer "what is your volume?" in tetravolumes. I've wondered about using 4 planes positioned at 60 degrees (ala the walls of a tetrahedron), each slidable to provide a tetrahedron's size and position (inside-outing also doable). The tetrahedron would be a kind of ``cursor'' in that it would imply a complex internal structure of selectable objects e.g. the ``cosmic hierarchy'' of concentric polys would be illuminable within tetrahedron X located in my 4D cross-hairs. Another cool interface would be 4D LOGO, a turtle-based language wherein the (multiple) turtles would be piloted to jump vectorially in an iso- tropic vector matrix (high rez). Polyhedra could be generated as successive turtle moves. ==================== End Kirby's response ==================== Steve Mather responded too: ==================== Begin Steve's response ==================== To continue the post on synergetic graphics, someone mentioned the possibility of finding the IVM inherent within the computer system. My first thought was that this was carrying things a little bit too far. There may be thousands of identical and "equidistant" on/off storage spaces within the computer, but the coordination of these into a visible IVM seems far too complex (though this may not have been the original line of thinking involved.) But then, thinking about the irrationality of using an in place XYZ coordinate system, struck upon the thought that such a system is ideal. The XYZ coordinate system is simply a center-bodied spherical octahedral set-up. As such, it is a truncated tetrahedron. From there, the breakdown is simple, and whole numbered. The octahedron (like its diamond relative) breaks down into the IVM, and can be formed into the icosahedron, the cube, and the vector equilibrium (the last facilitating cubic closest packing.) >From there (so far as I can see it,) everything falls into place and three-dimensions (or perhaps more appropriately-- four). ==================== End Steve's response ==================== Robert L. Read posts: Graphics applications on modern computers represent complicated "scenes" using millions of polygons, and the 3D virtual realities that are expected use billions of polygons per second. All of these polygons are generally represented in a pretty silly way: as list of floating points values. So modern graphics applications pump giant lists of floats over networks, off disks, around in memory, and perform X-illions of floating point values, which actually require special hardware built into chips. This does not seem a solution worth of design scientists. A more Fulleresque approach would be to represent objects directly as polyhedra. The polyhedra would be numbered (coded) using some numbering scheme that I can't imagine. But a given set of points in space would have a pyramid of representations, that are progressively more and more precise. Geometric computations could be performed at any precision level. (This is in fact already done in graphics applications in a relatively ad hoc way; algorithms often see if a "bounding box" intersects before attempt to determine if two polyhedra really intersect. Myriad other techniques are used.) For instance, a set of polygons defining a complex shape like Madonna's face could be first coded as a geodesic sphere of a given radius and center point. Then with each step down the precision pyramid, the geometry becomes more complicated and precise. The nose becomes a tetrahedron. The eyes are first dimples in the head, and then dimples filled with spheroids for the eyeballs, etc. How compact could such an encoding be? My suspicions are that it could be very compact. Could we construct algorithms that operate on these representations to do all the things done by computer programs on more conventional representations that would be as good or better than those representations? I believe that it is a possibility, and the improvement in computer graphics might be as to current approaches as the geodesic dome is to rectillinear structures. The notion of choice of precision has to be made for computer graphics just as it most be made for steel domes and trusses. An average screen only has 1 million pixels to be colored, and so many "scenes" are clearly over-specified, in the sense that many different scenes would look exactly the same when viewed on a 1 million-pixel display. For many applications, an order-of-magnitude improvement is needed. Photo-realistic rendering can take minutes or hours for a single picture to be computed. I find the application of Fuller's philosophy to Computer Science fascinating, although, in my mind, it is not as satisfying as physical design work, because although information and entertainment are important needs (even in Fuller's own research plan) seeing Madonna in 3D is not very important if you don't have a place to live or enough to eat. ================ Appendix: FAQ excerpt on programs available Computer tools (may or may not be useful to dome design or synergetics' modeling). I'm just getting up to speed with GNU-Calc (only runs under GNU Emacs) and gnuplot for graphs (these are available by anonymous ftp from prep.ai.mit.edu:pub/gnu/calc-2.02c.tar.gz and ftp.dartmouth.edu:/pub/gnuplot/gnuplot3.5.tar.Z. Pari-GP is a very good high-precision calculator tool for Unix, DOS, MS-Windows, Macs, Atari, Amiga, and even VAXen. It is available by ftp from megrez.ceremab.u-bordeaux.fr:/pub/pari. Also, POV-Ray is good for generating photo-realistic (or simply perspective) images. For those of us in poverty, there are many high-quality freeware programs for graphics work. When I've tested more of them, I'll be letting you know about them. If you have lots of money, many people rave about Mathematica and its competitor Maple. [From The Geometry Center, 22 JUN '92] The Geometry Center announces release 1.1 of geomview, a program for looking at and interactively manipulating 3D objects. The current version runs on Silicon Graphics IRIS workstations. It is available via anonymous ftp at geom.umn.edu(128.101.25.31):/pub/geomview/geomview-bin.tar.Z for pre- compiled binaries and documentation. The source distribution is geom.umn.edu(128.101.25.31):/pub/geomview/geomview.tar.Z and takes up 21 MB of disk space. [From Chris Fearnley] BTW, you can find out more about the Geometry Forum by e-mail (annie@forum.swarthmore.edu) or checking our their newsgroups geometry.whatever or they even advertise a 800 number ( 1-800-756-7823). [From the POV-RAY FAQ] * GEODOME1.ZIP - Utility for generating geodesic domes. Output to POV-Ray 2.x format as either facets or a mesh of pipes and joints. IBM PC executable, with source included. This gets my vote, but then it would _..._ (1994, Wardley) [From Ben Discoe] Anyone interested in the geometry mentioned in _Synergetics_ (and has access to a computer running 3D Studio R3) could check out a free program (on the net as HEDRA.ZIP) which purports to create a very wide variety of polyhedral forms. I don't think 3D Studio will let you easily raise the forms to higher frequencies, though. [From Kirby Urner] I've seen some interesting Synergetics on the Mac: Yasushi Kajikawa did a new module system for assembling icosahedra and other shapes in that 5-fold symmetric family -- 5-fold stuff is IN these days. He used HyperCard with XMD calls to MacroMind Director I think it was -- the individual movie frames were developed in Mathematica. Lots of polyhedra exploding into parts -- looked like car repair manuals for abstract geometric shapes. Music too. The text was all in Japanese. Robert Orenstein tried to get an English edition together -- he also got a jitterbug transformation to run entirely from within Mathematica. Looked cool! [From Robert L. Read] `FElt' is a structural analysis program that is freely available under the GNU Public License (GPL). It is written and maintained by Jason Gobat (jgobat@ucsd.edu) and Darren Atkinson (atkinson@ucsd.edu). It allows you to input a geometry of a structure, assign material types to various components, add on continuous forces like roof loads and specific forces like a 10,000 pound weight at a certain point, and then compute the forces in each member. [Editor: FElt is available for anonymous ftp at cs.ucsd.edu:pub/felt. For Linux users a binary is on sunsite.unc.edu in /pub/Linux/apps/math/felt-2.0.tar.gz.]/ ========================================================================= Date: Thu, 15 Sep 1994 08:40:39 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Bill Long Organization: SUNY at Plattsburgh, New York, USA Subject: Re: 'revolutionary' discussion groups >Date: Wed, 14 Sep 1994 16:11:11 -0500 >From: Mark Stowe >Subject: 'revolutionary' discussion groups > >As much as I like most of the political commentary here I am really looking >for a list or lists where folks are batting around very specific ideas >about exactly how future egalitarian ecotopian Fulleresque on-line >communities might work. Any one have any suggestions? Well, although not specific to the topic you're interested in, the HIT list is a forum for the discussion of Highly Imaginative Technology (and scifi). They are pretty receptive to just about any futuristic topic, like floating cities and such. You can subscribe via bitnet by sending the message: SUBSCRIBE HIT to LISTSERV@UFRJ If you are subscribing via internet then you must use e-mail to the address: LISTSERV%UFRJ.BITNET@CUNYVM.CUNY.EDU and put the command as the body of your message. Another list I read, the Electric Vehicle discussion group has started up a thread about using tensegrity structures for lightweight, sturdy frames. I think Bucky would've been proud. (is it true he was a less than exciting speaker?) Bill Long >--StarGazer ========================================================================= Date: Fri, 16 Sep 1994 18:47:00 -0400 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Searchnet Zec Organization: Channel 1(R) 617-864-0100 Info Subject: SearchNet 5085866977 This BBS / Net / Mailing list message is being posted for informational purposes in echoes related to info shared in Searchnet. I am available to respond to replies. In no way should this message be considered an 'attack' of any kind against a conference or network. My interest is in sharing info only. 508-586-6977 (XBN BBS, SearchNet HeadQuarters) 617-961-4865 International Searching For Your Individual PATH Network. The SearchNet network is for people to share information via modem. We are presently looking to add new members to carry our conferences, to ensure _reliable_ connections throughout the many changes expected to occur in telecommunications. Although some of our message areas are currently available in other networks, such as Mufonet, Internet, and Fidonet, we still need hubs and nodes ready to make mail available, in case any significant changes are made in existing connections. If you are already carrying some SearchNet echoes within another network, please consider signing up for a Searchnet node number. You will still get the echoes from your existing feeds, but will _already_ be connected in the event of any changes. Since March 1993, SearchNet has been providing a wealth of information on the status of our existence and Planet Earth. In the last 17 months, we have reached a point, where SearchNet has made a _significant_ impact on the telecommunications world. 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If people who benefit from the sharing of information within SearchNet do not actively _do_ something to continue it's existence, they will lose this resource. A word to the wise, should be sufficient. It _is_ time. * SOME * of the available SEARCHNET Message Conferences I_UFO UFO and New Science EARTH_CHANGES The Current Earth Changes and Transformation WORLD_NEWS Reports of significant World Events and Weather CHANNELS Messages from the spirit planes, and Channellers. Discussions of personal growth and transformation. ORVOTRON_PUB Public conference for Orvotron activities. Orvotron is The East Coast PowerPoint, a Tranformational Vortex! The site has a 39 foot Pyramid! Moderated by Walter Bartoo AKA Kortron NIGHT_SHIFT Independent NWO discussion based on Art Bell Radio Show SNET-L Our internet Mailing List covers all the above in one echo! Here are some of the topics: UFO's, Extra-terrestrials, contactees, abductees. 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QWK format mail exchange is also available for sysops AND users. -------------------------------------------------------------------- FTP privacy.com pub/glenda GLENDA STOCKS | FidoNet 1:330/201.0 SearchNet HeadQuarters | InterNet GS@rochgte.fidonet.org Snet Mailing List info, SEND | Data: 508-586-6977 / 617-961-4865 info snet-l TO | Download SEARCHNT.ZIP For Info! majordomo@world.std.com | Voicemail: +1-617-341-6114 Searchnet.zec@channel1.com | FidoNet CHANNELS, & I_UFO moderator * RM 1.3 00257 * You're invited to the wedding; Science and Spirituality! ========================================================================= Date: Fri, 16 Sep 1994 19:35:44 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: Graphics -- Synergetics ftp site? Thanks, Chris, for the excellent summary of the programming software for synergetics graphics thread. Richard <> has been sending me both stills and moving pictures. He patiently worked out the kinks involved in going from his Mac to my Windows platform. I've made some of his images into a slide show which doubles as my Windows screen saver. Ultra cool.[1] Movies in "flattened QuickTime format" can be taken from a Mac and played using EDRIVE, a shareware viewer downloadable via CompuServe (EDRIVE forum). Richard's movies are of his intriguing explorations using Quadrants. The toy and "artifical heart" especially caught my fancy. This brings us to the question of an ftp site. Apparently the Synergetics Institute in Japan has access. I noticed tensegrity.jpg and curVE.jpg files available via http://cs1.sfc.keio.ac.jp/~t93827ya/dome/dome.html plus mention of an actual ftp site. Unfortunately, I come up against a lot of dead ends when trying to click around from here. 'Anonymous login not accepted' and so on. [1] for turning jpg files into screen savers and wallpaper in Windows, I highly recommend the product from Second Nature Software "a company dedicated to helping fund environmental and other non-profit oragnizations and promoting the works of talented artists and photographers." (BBS 503 221 8744 10 lines, 2400-14.4 N81). ------------------------------------------------ Kirby T. Urner pdx4d@teleport.com 4D Solutions (teleport.com = public access node) Portland (PDX), Oregon "All realities are virtual" -- KU ========================================================================= Date: Fri, 16 Sep 1994 23:25:24 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Software, Graphics Continuing this thread on graphics.... For those of you maybe lucky enough to run NeXT or Sparc stations, there's a 3D (Fuller: 4D) geometry viewer out there. Would be useful for sharing synergetics. For more info, World Wide Web browsers: http://www.geom.umn.edu/docs/software/viz/geomview/geomview.html Looks like the Synergetics Institute is only a mouse click away (links between Geometry Center and Japan look strong). Shared with Yoshiaki Araki about my interest in finding an ftp site for synergetics imagery. Japan's HTML scene looks pretty interesting. Invitations to download 38 megabyte quicktime movie of popular TV comedy show. I don't think so.... Any readers of Wired out there? "Military maneuvers are no longer about dispersing the fog of war, but about stage-managing the special effects. Combining Disney- land, Hollywood, and Silicon Valley, the National Training Center, full of video cameras and computerized special effects, not to mention thrilling rides, has superseded Los Alamos and the Nevada Test Site to become the premiere production set for the next generation of strategic superiority" Cyber-deterrence, pg. 158 (Wired, Sept 1994) That's our World Game budget, going up in smoke and mirrors. Talk about Hollywood-style media extravaganzas. What we need to enlist the imaginations of would-be world game players in the Design Science agenda is some eye popping simulations, using real props, ready for field testing. Some of that is going on vis-a-vis the tortoises at Fort Irwin -- "The scientists claimed to be matching the warfighters chip for chip in the information war. Tortoises [endangered species in the Fort terrain] were tagged with transmitters, tracked by radio telemetry, and graphed in grid locations by computers." (ibid) Same technology, used as livingry instead of killingry. On the eve of what looks like another media extravaganza orgy of military might, lets remember Fuller's nationless icosamap and the concept of networking for livingry, not political scenarios of death and mayhem. Haitians would do better in a future with the World Livingry Service industry than without. ------------------------------------------------ Kirby T. Urner pdx4d@teleport.com 4D Solutions (teleport.com = public access node) Portland (PDX), Oregon "All realities are virtual" -- KU ========================================================================= Date: Sat, 17 Sep 1994 19:56:22 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Jim Bowery Organization: NETCOM On-line Communication Services (408 261-4700 guest) Subject: Ron Resch's geometry of folds Is anyone familiar with Ron Resch's geometry of folded surfaces? It seemed to have a universal character similar to RBF's geometries, but somehow it didn't catch on with the popular culture to nearly the extent. -- The promotion of politics exterminates apolitical genes in the population. The promotion of frontiers gives apolitical genes a route to survival. ========================================================================= Date: Fri, 16 Sep 1994 23:06:00 -0400 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Searchnet Zec Organization: Channel 1(R) 617-864-0100 Info Subject: PolyWog CF> The modeller is called "PolyWog", and it's currently freeware CF> (I'm a "revolutionary" too :-) I'm considering copylefting it.'' I am new here, but is there an ftp site for this program? Time to go! Glenda GLENDA STOCKS | FidoNet 1:330/201.0 SearchNet HeadQuarters | InterNet GS@rochgte.fidonet.org Snet Mailing List info, SEND | Data: 508-586-6977 / 617-961-4865 info snet-l TO | Download SEARCHNT.ZIP For Info! majordomo@world.std.com | Voicemail: +1-617-341-6114 Searchnet.zec@channel1.com | FidoNet CHANNELS, & I_UFO moderator * RM 1.3 00257 * If you believe in telekinesis, raise my hand. ========================================================================= Date: Fri, 16 Sep 1994 23:08:00 -0400 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Searchnet Zec Organization: Channel 1(R) 617-864-0100 Info Subject: World Game DW> We currently have posted on our bulletin board a letter from a DW> woman whose father-in-law expressed a desire before he died that DW> his grandchildren participate in a grade school version of the DW> workshop he had observed. howdy, sorry to butt in. May I call your BBS? Do you have other information on it about Bucky's work? Glenda GLENDA STOCKS | FidoNet 1:330/201.0 SearchNet HeadQuarters | InterNet GS@rochgte.fidonet.org Snet Mailing List info, SEND | Data: 508-586-6977 / 617-961-4865 info snet-l TO | Download SEARCHNT.ZIP For Info! majordomo@world.std.com | Voicemail: +1-617-341-6114 Searchnet.zec@channel1.com | FidoNet CHANNELS, & I_UFO moderator * RM 1.3 00257 * A Black Hole 2 Miles Wide? That would really Suck! ========================================================================= Date: Sat, 17 Sep 1994 08:12:00 -0400 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Searchnet Zec Organization: Channel 1(R) 617-864-0100 Info Subject: Fog Gun anyone? CF> Here is what I've compiled on the fog gun from the FAQ: howdy, Where may I ftp this FAQ? Time to go! Glenda GLENDA STOCKS | FidoNet 1:330/201.0 SearchNet HeadQuarters | InterNet GS@rochgte.fidonet.org Snet Mailing List info, SEND | Data: 508-586-6977 / 617-961-4865 info snet-l TO | Download SEARCHNT.ZIP For Info! majordomo@world.std.com | Voicemail: +1-617-341-6114 Searchnet.zec@channel1.com | FidoNet CHANNELS, & I_UFO moderator * RM 1.3 00257 * I don't have a ride, so I'll walk... *POOF* ========================================================================= Date: Sun, 18 Sep 1994 07:58:00 -0400 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Searchnet Zec Organization: Channel 1(R) 617-864-0100 Info Subject: C60's uncanny strength GS> Here is an example of practical applications found from GS> theories derived by looking at shapes; the pre-existing GS> patterns of creation. Although Buckminster Fuller may not have GS> used the term 'sacred geometry', that is the kind of geometry GS> he did. ------------------------------------------------------------ TI : THE LEADERS OF SCIENCE The Readers of THE SCIENTIST PG : 8 RICHARD E. SMALLEY Gene and Norman Hackerman professer of chemistry and professor of physics, Rice University, Houston. Richard Smalley believes that "science is a crucial enterprise, not just to keep us economically competitive with other nations but, more important, to develop practical solutions to the dilemmas facing society." In his Rice University laboratory, Smalley developed a new technology-- supersonic cluster beams -- that enables a more detailed understanding of polyatomic structures. This technology provided an unprecedented look at the structure and character of chemical bonds in larger molecules. This research also led to the discovery of C60, the third elemental form of carbon in addition to diamond and graphite, in 1985. A soccer-ball-shaped molecule, C60 is known as buckminsterfullerene, or "buckyball," because its structure resembles the geodesic domes made famous by R. Buckminster Fuller. Smalley is currently concentrating on producing continuous carbon fibers, which essentially are giant single fullerene molecules. Just a few nanometers wide but many centimeters long, the fullerene fibers are expected to be the strongest fibers ever manufactured, perhaps 100 times stronger than steel. When eventually produced in large quantities, fullerene fibers promise to have widespread practical applications in the chemical, automotive, aerospace, and other major industries. Throughout his distinguished research career, Smalley has maintained a strong commitment to teaching. This year, he is teaching freshman chemistry to help inspire the next generation of scientists and educators. He has also succeeded in making Rice an important center for basic research, having founded the interdisciplinary Rice Quantum Institute in 1979. Despite his demanding schedule, Smalley takes the time to read THE SCIENTIST. He says "THE SCIENTIST is fun to read, topical, and up to date. It tells you about the interesting people who do science, as well as their interesting results." (The Scientist, Vol:8, #17, pg.8 , September 5, 1994) (Copyright, The Scientist, Inc.) ---------- WE WELCOME YOUR OPINION. IF YOU WOULD LIKE TO COMMENT ON THIS STORY, PLEASE WRITE TO US AT EITHER ONE OF THE FOLLOWING ADDRESSES: garfield@aurora.cis.upenn.edu 71764.2561@compuserve.com The Scientist, 3600 Market Street, Suite 450, Philadelphia, PA 19104 U.S.A. -------- GLENDA STOCKS | FidoNet 1:330/201.0 SearchNet HeadQuarters | InterNet GS@rochgte.fidonet.org Snet Mailing List info, SEND | Data: 508-586-6977 / 617-961-4865 info snet-l TO | Download SEARCHNT.ZIP For Info! majordomo@world.std.com | Voicemail: +1-617-341-6114 Searchnet.zec@channel1.com | FidoNet CHANNELS, & I_UFO moderator * RM 1.3 00257 * We've replaced the dilithium with Folgers Crystals! ========================================================================= Date: Sun, 18 Sep 1994 19:43:55 -0400 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "" Subject: More Tensegrity Fasteners A quick note - regarding connection mechanisms for small tensegrities, which has been, and continues to be, an interest of mine. I've located another fastener for monofilament based constructions; it can be purchased at mass market and sporting goods stores, under the name 'Not-A-Knot', produced by Berkley Outdoor Technologies Group. (I'm not associated with them in any way.) The thing is a double-ended wire loop which looks something like this: _ __ / \ \ / \ / \ / / / \ \ _ / / / \----------------------------/--------/ / ^------------- about 2cm ----------------^ A loop of monofilament is hung on the crook formed at the left loop. Both tails of the monofilament loop are then wrapped around the straight portion for five turns; the direction does not matter. The (doubled-up) line is then pulled tight (it moves into the loop on the right), and (either) one of the remaining monofilaments is trimmed of excess. I do not know if this is under a patent of any kind, or even if this is new or a well-known method of tying lines. What is significant: 1. My tests with 25lb test and 8lb test showed the connection to be stronger than the line (the lines failed at points other than the N.A.K.) 2. It appears to be easier to determine the the length of a cable terminated with N.A.K.'s than with ordinary monofilament knots, since with most knots it is difficult to determine where they will finally tighten up. ------------------------------------------------------------------------- Mitch C. Amiano amiano@delphi.com ========================================================================= Date: Mon, 19 Sep 1994 12:24:21 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kiyoshi Kuromiya Subject: Re: 'revolutionary' discussion groups X-cc: rich@cpp.pha.pa.us In-Reply-To: from "Bill Long" at Sep 15, 94 08:40:39 am Bucky Fuller was an exciting speaker. Many however found some of his verbal shorthand ("thinking aloud") confusing because he covered so much terrritory in a three-hour talk. By the end of the three-hour talk, he was usually able to resolve all the discussion threads and tie everything into a neat bundle. Because individuals may not believe such a prodigious feat possible, they may have dismissed what seemed at first to be disorganized ramblings. Some familiarity with Fuller's use of words and his basic premises always helped one navigate one of his marathon three- or four-hour talks, or his 43-hour talks in which he says he can communicate everything he knows (that only he talks about). He treated his thinking out loud as a very specific discipline, similar to Percival Bridgman's description of Einstein's operational technique which used a blackboard to map out in logical sequence an idea and the consequences. -- Kiyoshi Kuromiya Forwarded message begins here. > > >Date: Wed, 14 Sep 1994 16:11:11 -0500 > >From: Mark Stowe > >Subject: 'revolutionary' discussion groups > > > >As much as I like most of the political commentary here I am really looking > >for a list or lists where folks are batting around very specific ideas > >about exactly how future egalitarian ecotopian Fulleresque on-line > >communities might work. Any one have any suggestions? > > Well, although not specific to the topic you're interested in, the HIT list > is a forum for the discussion of Highly Imaginative Technology (and scifi). > They are pretty receptive to just about any futuristic topic, like floating > cities and such. You can subscribe via bitnet by sending the message: > SUBSCRIBE HIT to LISTSERV@UFRJ > If you are subscribing via internet then you must use e-mail to the address: > LISTSERV%UFRJ.BITNET@CUNYVM.CUNY.EDU > and put the command as the body of your message. > > Another list I read, the Electric Vehicle discussion group has started up a > thread about using tensegrity structures for lightweight, sturdy frames. I > think Bucky would've been proud. > > (is it true he was a less than exciting speaker?) > > Bill Long >--StarGazer > ========================================================================= Date: Mon, 19 Sep 1994 10:47:36 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: smtc5@UOFT02.UTOLEDO.EDU Organization: University of Toledo Subject: Re: 'revolutionary' discussion groups In Article <9409141934.AA12259@monarch.zoo.ufl.edu> Mark Stowe writes: >>> >>>The problem with revolutions is that they have a strong tendencies >>>to leave many problems unsolved while at the same time facilitating >>>the installation of a censurious - if not dictatorial - leadership. >>> > >As much as I like most of the political commentary here I am really looking >for a list or lists where folks are batting around very specific ideas >about exactly how future egalitarian ecotopian Fulleresque on-line >communities might work. Any one have any suggestions? Just stick around. We'll broach the topic sometime or another.... Steve Mather ========================================================================= Date: Tue, 20 Sep 1994 01:26:44 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Dane Winberg Organization: Drexel University Subject: Re: World Game > DW> We currently have posted on our bulletin board a letter from a >howdy, sorry to butt in. May I call your BBS? Do you have other >information on it about Bucky's work? >Glenda I should watch my language. I was talking about a non-virtual bulletin board. Cork, thumbtacks, wood frame...like that.(Though some would say all bulletin boards are virtual...) Dane ========================================================================= Date: Tue, 20 Sep 1994 16:41:28 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Gary Lawrence Murphy Organization: Ontario Science Centre Research & Exhibit Planning Subject: The Revolution will not be televised (was Re: 'revolutionary' discussion groups) In-Reply-To: smtc5@uoft02.utoledo.edu's message of Mon, 19 Sep 1994 10:47:36 GMT Greetings to all children of the revolution ;-) SM> In Article <9409141934.AA12259@monarch.zoo.ufl.edu> Mark Stowe SM> writes: >>>> The problem with revolutions is that they have a strong >>>> tendencies to leave many problems unsolved while at the same time >>>> facilitating the installation of a censurious - if not >>>> dictatorial - leadership. Tell it to Eli Whitney, master revolutionary leader! In article smtc5@uoft02.utoledo.edu writes: >> As much as I like most of the political commentary here I am >> really looking for a list or lists where folks are batting around >> very specific ideas about exactly how future egalitarian ecotopian >> Fulleresque on-line communities might work. Any one have any >> suggestions? > "SM" == smtc5 writes: SM> Just stick around. We'll broach the topic sometime or another.... SM> Steve Mather One hot midsummer day, Dogen was out walking in the garden when he came upon the old gardener busily sweeping the garden path. Dogen asked the gardener why he was doing this labour in the heat of the sun, to which the gardener replied, "If not now ... when?" :-) Case after case in a thousand points tell us "Political solution" is an oxymoron. Real revolution is as simple as the Cotton Gin, the thimble, the paper-clip or the wireless. Worlds of commentary and discourse run counter to the Guinea-Pig "B" experiment. "How might the 'future egalitarian ecotopian Fulleresque on-line communities' work?" needs to be rephrased as "What needs doing now?", for if Bucky (or any of us) did not live out his days in that FEEFOLC ;-), exactly where _did_ he live? I'm no athelete, but one of my fave media voices, NIKE, puts it best: Just do it. (their new Burroughs spot is even better ;-) Journey of a thousand miles and all that --- or to wax even more philosophic, I quote Drake Puddleduck ;-) ... "It's a perfectly fine morning!" :-) -- Gary Lawrence Murphy ----------------------------- garym@199.212.12.1 Ontario Science Centre ---- 770 Don Mills Road ---- Don Mills M3C 1T3 Research/Exhibit Planning --------------- voice: (416) 429-4100 x2215 --------- Problems worthy of attack prove their worth by hitting back ========================================================================= Date: Tue, 20 Sep 1994 11:34:00 -0400 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Searchnet Zec Organization: Channel 1(R) 617-864-0100 Info Subject: PI without Trig From: arnith@ismennt.is (Arni Thoroddsen) Subject: PI without Trig Date: Tue, 20 Sep 1994 04:27:32 +0000 (GMT) >I've stumbled upon a mystery which I hope someone here can help me >solve. Unfortunately, it's quite detailed, so I hope you'll bear with >me during the explanation. Here goes: > [some stuff ommitted] >NB actually, I filled only the upper hemisphere with cylinders, and >multiplied their volumes by 2. The following diagram is supposed to >resemble the hemisphere filled with 4 cylinders. My program used >10,000 cylinders, but drawing that was out of the question. As someone >said earlier, "I hate ascii". > > __.__.__ > _.|________|._ > .|______________|. > .|__________________|. >.|____________________|. > > >The resulting sum of volumes agreed quite closely to the valued given >if you use the standard formula for the volume of a sphere: > >Vsphere = (4/3)PI*Radius*Radius*Radius = 4.1887902 > (my program said Vsphere was equal to 4.1887901) > >Encouraged by this result, I modified the program to calculate the >area of each cylinder wall. The sum of all 10,000, I thought, should >be a good approximation of the surface area of the sphere. (of some >interest to people who design domes, yes?) > >The equation for the Surface Area of a Sphere said: >SAsphere = 4*PI*Radius*Radius = 12.5664 > >But my program said SAsphere = 9.8696 > >The error is more than 20% !! This was surprising, considering the >accuracy I had achieved with my sphere-volume program. So I thought up >a *new* algorithm. It is easy to explain this result. If you take the radius of each puck and give it the height of the as witdth, you get a plurality of strips, piled on top of each other in a stepwise manner. These radius steps form a quarter of a circle (picture this stepwise quarter circle in you mind). Now if you multiply any of these radius strips by the constant 2*PI, you will get the surrounding area of the corresponding puck (strip). Now the area of the stepwise quarter circle is very very close to the area of a quarter circle which is PI/4 since the radius is 1 in length. Now if you multiply each of the radius strips by the constant 2*PI (or any constant in fact) it would be close to equivalent to multiplying the area of the quarter circle by the same constant. Thus: (Area of all puck strips) = (area of 1/4circle * [ 2 * PI ] = PI/4 * [ 2 * PI ] and this is clearly eaqual to PI * PI /2. You do the same for the lower half of the sphere and you wind up with a total area of PI * PI when you add both areas. So this should solve that little mystery > >ALGORITHM #2 > >- Start with a hemisphere (radius=1). >- Draw a line from the north pole to the equator. >- Move a very small distance along the equator, then draw a second > line from the north pole to this new point on the equator. > >We have just drawn a long, skinny isosceles triangle. It's base is on >the equator, and it's apex is at the north pole. > >Now we cover the entire surface of the hemisphere with triangles >identical to the one just described. (Before beginning, we cleverly >ensured that the base of the triangle would be some integer fraction >of the distance around the equator, say 1/1000th.) Each apex lies at >the north pole, and each base lies along the equator. The triangles do >not overlap, and they cover the hemisphere completely. I must be misunderstanding what you are doing here since it seems like you are approximating the area of a cone that has the equator as its base and the pole as its top. But in that case you I think you should be getting another result. Actually I am grappling with the 4 dimensional versions of this stuff, and frankly I am not making much progress in doing it without resorting to calculus. I figured if Archimedes could do it in 3 dimensions, why not try it in 4 using similar deductive methods. Of course Archimedes was no slouch in the geometric visualisation department. But resorting to calculus seems to me to be cheating somehow. ----- Arni Thoroddsen arnith@ismennt.is Fjolugata 19, Reykjavmk, Iceland GLENDA STOCKS | FidoNet 1:330/201.0 SearchNet HeadQuarters | InterNet GS@rochgte.fidonet.org Snet Mailing List info, SEND | Data: 508-586-6977 / 617-961-4865 info snet-l TO | Download SEARCHNT.ZIP For Info! majordomo@world.std.com | Voicemail: +1-617-341-6114 Searchnet.zec@channel1.com | FidoNet CHANNELS, & I_UFO moderator * RM 1.3 00257 * And these Things Shall Come to Pass.... ========================================================================= Date: Wed, 21 Sep 1994 10:48:06 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Larry Calvert Organization: Internet On-Ramp, Inc. Subject: WANTED: Geodesic Dome Books [ Article crossposted from alt.books.technical ] [ Author was Larry Calvert ] [ Posted on 21 Sep 1994 10:39:11 -0700 ] I am looking for books dealing with Geodesic Domes. Please email me if you have any available or know where I might find some. Thanks, Larry Calvert larryc@on-ramp.ior.com ========================================================================= Date: Wed, 21 Sep 1994 23:03:22 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kiyoshi Kuromiya Subject: Re: The Revolution will not be televised (was Re: 'revolutionary' X-cc: rich@cpp.pha.pa.us In-Reply-To: from "Gary Lawrence Murphy" at Sep 20, 94 04:41:28 pm > > Greetings to all children of the revolution ;-) > > SM> In Article <9409141934.AA12259@monarch.zoo.ufl.edu> Mark Stowe > SM> writes: > >>>> The problem with revolutions is that they have a strong > >>>> tendencies to leave many problems unsolved while at the same time > >>>> facilitating the installation of a censurious - if not > >>>> dictatorial - leadership. > > Tell it to Eli Whitney, master revolutionary leader! > > In article smtc5@uoft02.utoledo.edu writes: > >> As much as I like most of the political commentary here I am > >> really looking for a list or lists where folks are batting around > >> very specific ideas about exactly how future egalitarian ecotopian > >> Fulleresque on-line communities might work. Any one have any > >> suggestions? > > > "SM" == smtc5 writes: > SM> Just stick around. We'll broach the topic sometime or another.... > SM> Steve Mather > > One hot midsummer day, Dogen was out walking in the garden when he > came upon the old gardener busily sweeping the garden path. Dogen asked > the gardener why he was doing this labour in the heat of the sun, to which > the gardener replied, "If not now ... when?" :-) > > Case after case in a thousand points tell us "Political solution" is > an oxymoron. Real revolution is as simple as the Cotton Gin, the > thimble, the paper-clip or the wireless. Worlds of commentary and > discourse run counter to the Guinea-Pig "B" experiment. > > "How might the 'future egalitarian ecotopian Fulleresque on-line > communities' work?" needs to be rephrased as "What needs doing now?", > for if Bucky (or any of us) did not live out his days in that FEEFOLC > ;-), exactly where _did_ he live? > > I'm no athelete, but one of my fave media voices, NIKE, puts it best: > Just do it. (their new Burroughs spot is even better ;-) > > Journey of a thousand miles and all that --- or to wax even more > philosophic, I quote Drake Puddleduck ;-) ... > > "It's a perfectly fine morning!" :-) > > -- > Gary Lawrence Murphy ----------------------------- garym@199.212.12.1 Gary-- You are cordially invited to visit our online community--Critical Path AIDS Project BBS and Fuller Information Exchange BBS (215) 463-7160. We publish Critical Path AIDS Project newsletter, a treatment newsletter for persons with AIDS, now in its 5th year of publication. We are, without the self-conscious rhetoric, quietly putting together the infrastructure for a global virtual community such as you propose. Within 60 to 90 days, we will be an Internet host with 8 phone lines (all 28.8 k modems) and 2.6 gigabytes of online database storage. Our UnixWare operating system operates on a 16 mb RAM, 50 mHz Micronics motherboard. We will provide, to the extent we can, a "free net" for residents of the Philadelphia area, while at the same time provide our online databases and discussion groups to the Internet. Visit and register for a shell account. Please excuse us, during our year-long upgrade of our equipment, software, interface, and services. --Kiyoshi Kuromiya ========================================================================= Date: Thu, 22 Sep 1994 10:45:46 CST Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Tom Dosemagen Subject: Re: WANTED: Geodesic Dome Books Call natural Spaces at 800-733-7107. ========================================================================= Date: Thu, 22 Sep 1994 10:47:41 CST Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Tom Dosemagen Subject: Re: WANTED: Geodesic Dome Books I'm sure my first message got thru or not. Call Natural Spaces at 800-733-7107 and ask for their All About Domes Book. ========================================================================= Date: Thu, 22 Sep 1994 14:05:00 -0400 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "H. Jeffrey Rosen" Subject: Re: 'revolutionary' discussion groups Was Bucky an exciting speaker? At my college commencement in 1972, Bucky addressed the graduates and their parents. Some of the grads had read "Operating Manual" or "Nine Chains", and some were familiar with Synergetics. His chosen topic (which was a surprise to this audience... not too surprising for those of us who recall his style of discourse) was "No One Should Have To Work For A Living!" After the first 40 minutes, the students were spellbound, and the parents were getting restless. After the next hour, parents had begun to hold disruptive conversations in the theater. Some simply walked out. Several attempts were made to applaud Bucky off the stage. Whether he heard these insults or not is a matter for speculation, but the monologue continued. After two hours and fifteen minutes, the loose ends were tied up, and Fuller took his seat among my college administrators, who had been nervously glancing at their watches for ninety minutes. At that moment, the President of the senior class arose and, turning to Fuller, loudly apologized for the conduct of the parents and others who had tried to cut the address short. The graduating class applauded this gesture, but Fuller just smiled. Even without the suspenseful group dynamics, it was the gutsiest, and surely one of the most exciting speeches I have ever heard. But universal ideas take time to express, even when every word is costly. Does anyone on this list recall Bucky's famous telegram to Ed Muskie during the Presidential campaign of '72? HJ.ROSEN@SRS.GOV ========================================================================= Date: Thu, 22 Sep 1994 19:52:24 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Kevin Sahr Organization: Forest Sciences Laboratory Subject: Geodesic activity in Minnesota? I've heard that there is some activity going on in Minneapolis involving icosahedral sub-divisions of the earth. As this is something that we are working on as well, I wondered if anyone knew anything about this activity (we hate to duplicate work!). Thanks, Kevin ========================================================================= Date: Thu, 22 Sep 1994 21:43:57 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Glenda M Stocks Organization: The World Public Access UNIX, Brookline, MA Subject: new relativity theory I cam across an interesting post in physics.new-theories on something called NRG and basically it is exanding E=mc^2 to E=mc^3/3. But their theories mention sacred geometry, and that is an interest of mine, and I am studying Fuller's works, to see what he has that ties in with all of this. Anyways, I wanted to post the fellow's message here, but am loathe to get hate mail. If anyone is interested, lemme know, and I will post it as 3 short 80 line messages. The fellow claims that this new equation explains how the universe works, with an emphasis on geometry. Time to go! Glenda GLENDA STOCKS | FidoNet 1:330/201.0 SearchNet HeadQuarters | InterNet GS@rochgte.fidonet.org Snet Mailing List info, SEND | Data: 508-586-6977 / 617-961-4865 info snet-l TO | Download SEARCHNT.ZIP For Info! majordomo@world.std.com | Voicemail: +1-617-341-6114 Searchnet.zec@channel1.com | FidoNet CHANNELS, & I_UFO moderator * RM 1.3 00257 * My Akashic record is scratched, life keeps repeating itself. ========================================================================= Date: Fri, 23 Sep 1994 01:28:17 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Ross Keatinge Organization: Public Access Internet, Auckland New Zealand Subject: Re: WANTED: Geodesic Dome Books Tom Dosemagen (dosemagt@UWWVAX.UWW.EDU) wrote: : I'm sure my first message got thru or not. Call Natural Spaces at : 800-733-7107 and ask for their All About Domes Book. I am also interested in getting a copy. Do they have a normal phone or fax number ? 800 numbers can only be reached from a very small subset of the total surface area of Spaceship Earth. ;-) Thanks Ross ========================================================================= Date: Fri, 23 Sep 1994 08:47:24 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "Marvin G. Beshirs" Subject: Re: new relativity theory In-Reply-To: <9409222259.AA25950@ozarks.sgcl.lib.mo.us> I was wondering if the /3 applies to the exponent, the c^3, or the entire right side of the equation? I would be interested in this theory. You can email it to me personally if no one else is interestered. Thanks for bringing this out and whatever you send to me. May God be with you and yours. Don't criticize me too loudly until Marvin Beshirs (:> you have walked a mile in my shoes! e-mail at mbeshirs@ozarks.sgcl.lib.mo.us !Please! On Thu, 22 Sep 1994, Glenda M Stocks wrote: > I cam across an interesting post in physics.new-theories on something > called NRG and basically it is exanding E=mc^2 to E=mc^3/3. But their > theories mention sacred geometry, and that is an interest of mine, and > I am studying Fuller's works, to see what he has that ties in with all > of this. Anyways, I wanted to post the fellow's message here, but am > loathe to get hate mail. If anyone is interested, lemme know, and I > will post it as 3 short 80 line messages. The fellow claims that this > new equation explains how the universe works, with an emphasis on > geometry. > > Time to go! > Glenda > > GLENDA STOCKS | FidoNet 1:330/201.0 > SearchNet HeadQuarters | InterNet GS@rochgte.fidonet.org > Snet Mailing List info, SEND | Data: 508-586-6977 / 617-961-4865 > info snet-l TO | Download SEARCHNT.ZIP For Info! > majordomo@world.std.com | Voicemail: +1-617-341-6114 > Searchnet.zec@channel1.com | FidoNet CHANNELS, & I_UFO moderator > > * RM 1.3 00257 * My Akashic record is scratched, life keeps repeating itself. > ========================================================================= Date: Fri, 23 Sep 1994 14:30:47 GMT Reply-To: bcarroll@Eng.Sun.COM Sender: List for the discussion of Buckminster Fuller's works From: Bruce Carroll - Sun BOS Systems Product Assurance CONTRACTOR Organization: Sun Microsystems Inc. - BDC Subject: Re: WANTED: Geodesic Dome Books Here is a cardfile for Ms Windows that lists 17 different dome kits makers and plans. I compiled this in my search for domes, and ended up with getting blueprints from Key Dome (Miami, Fl), and am currently building my first dome from them. Bruce Carroll Virtual Mountain vmountain@aol.com <<--use this address, since my contract is up next week at Sun Fitzwilliam, NH ********************************************* BEGIN----------------------CUT HERE-------------------------- begin 644 domes.crd M34=#$0````````!Y`P```$%M97)I8V%N($EN9V5N=6ET>0`````````````` M````````````````````````!@0```!#87-C861E($1O;65S`&-T=7)E2!$;VUE`'!A8V4@1&]M97,````````````````` M````````````````````@`8```!+:6YG1&]M97,`;F=E;G5I='D````````` M`````````````````````````````/0&````36]N;VQI=&AI8R!#;VYS=')U M8W1O"`Q.3"`Y.#`T,C<-"DAO=7-T;VXL(%18(#2P@5%@@-S8V-3$- M"@T*.#`P+38P."TP,#`Q#0H-"B0Q.2XY-2!V:61E;R!B`%-H96QT97(@4WES=&5M"`T,#`-"E!I;F4@4FEV97(L(#0L($U.(#4V M-# Sender: List for the discussion of Buckminster Fuller's works From: Kirby Urner Subject: Re: Geodesic activity in Minnesota? >I've heard that there is some activity going on in Minneapolis >involving icosahedral sub-divisions of the earth. As this is something >that we are working on as well, I wondered if anyone knew anything >about this activity (we hate to duplicate work!). > >Thanks, > >Kevin > I got a call from David Koski who lives out there. I guess the U of M did a thing a year or so ago where kids in classrooms mailed in their icosa segments of global data, which was applied to an icosasphere. Segments that didn't look too good were airbrushed with clouds. David found this article about how this is being done again, now on a bigger scale. Some dude spearheading the project was claiming to have come up with the idea of an icosahedral projection while staring at a soccer ball in K-mart or something, no attribution to Fuller. I know this is vaguer than vague. David was going to fax me the newspaper article but turns out he threw it away. I wouldn't worry about duplicating anything. The more parallel efforts the better -- trial and error requires reinventing the wheel several dozen times before we get it down. ------------------------------------------------ Kirby T. Urner pdx4d@teleport.com 4D Solutions (teleport.com = public access node) Portland (PDX), Oregon "All realities are virtual" -- KU ========================================================================= Date: Fri, 23 Sep 1994 23:48:14 -0700 Reply-To: Ronald Reynolds Sender: List for the discussion of Buckminster Fuller's works From: Ronald Reynolds Subject: Re: SUMMARY: Computer Graphics and Mathematics Tools for Synergetics and Domes In-Reply-To: <199409150602.XAA05002@mail2.netcom.com> Thank you Chris for taking the time to compose this summary of computer Aided Geodesics. I'm an OOP programmer by profession, currently working on Apple's latest system software. Bucky, geodesics, and synergetics, have facinated me for many years. One thing I am sure of is that procedural approaches to the problem of synergetic modeling will not work. A procedural model would have to be way too complex. Object Oriented programming is much closer to the real world as we preceive it, i.e. the state of a thing and its behaviors are always presented together, never as an array of values and one or more processes that select from the array and then act on that selected data in a generic way. The moment you try to start special casing procedurally repesented data, the complexity of the task soon overwelms you. Trying to model relationships is even worse. Object Oriented techniques can express more that simple data/function relationships. Specificly, in OOP (Object Oriented Programming) you can express not only relationships between data and behaviors, but also realtionships between objects, or retationships between collections of objects. The present trend, at least in the C++ community, is toward models that are based on objects and collections of objects. A couple of contributers to Chris's summary mentioned OOP appoaches to represent Synergetic models. They all viewed the atomic objects as polyhedrons. The polyhedron is too course, and too finite for proper modeling. A better choice would be vectors and vertices. Aren't polyhedron made only of these? Using true atomic objects would allow us to model virtually any shape. We could model polyhedra as a collection of vertice objects, with each vertice object containing a collection of vectors that expressed the relationships with the other vector objects in the polyhedra's collection. The vertices would represent the event points and the vectors would represent their relationships. These tetrahedron objects could then be related in larger collections of virtually infinite complexity, even something as complex as Madonna's face. A final point; a vectice object, with the help of his vector objects, could easily provide the structure and behaviors to convert from an xyz coordinate system to one based on some other space model. We just need to figure out what our positional reationship model will be and the conversions between it and the XYZ coordinate system. That doesn't sound all that difficult to me. Let's talk about this more. It's a very exciting, fundamental subject. Ron Reynolds ========================================================================= Date: Sat, 24 Sep 1994 14:06:00 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Bob Hiltner Organization: Eskimo North (206) For-Ever Subject: Re: new relativity theory Glenda M Stocks (snet@world.std.com) wrote: : I cam across an interesting post in physics.new-theories on something : called NRG and basically it is exanding E=mc^2 to E=mc^3/3. But their : theories mention sacred geometry, and that is an interest of mine, and : I am studying Fuller's works, to see what he has that ties in with all : of this. Anyways, I wanted to post the fellow's message here, but am : loathe to get hate mail. By all means Glenda. This sounds interesting. : GLENDA STOCKS | FidoNet 1:330/201.0 Bob Hiltner "It is not enough to do well (and I hope you do), you must also do good" ^^^^ ========================================================================= Date: Sun, 25 Sep 1994 02:32:35 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Glenda M Stocks Organization: The World Public Access UNIX, Brookline, MA Subject: new relativity theor MM> I was wondering if the /3 applies to the exponent, the c^3, or MM> the entire right side of the equation? the whole thing is /3. I sent it to you. He says to multiply e=mc^2 by c/3 . Time to go! Glenda GLENDA STOCKS | FidoNet 1:330/201.0 SearchNet HeadQuarters | InterNet searchnet.zec@channel1.com Snet Mailing List info, SEND | BBS: 508-586-6977 / 617-961-4865 info snet-L TO | Download SEARCHNT.ZIP For Info! majordomo@world.std.com OR | Voicemail: +1-617-341-6114 subscribe snet-L "address" | FidoNet CHANNELS, & I_UFO moderator * RM 1.3 00257 * A seminar on Time Travel will be held 2 weeks ago ========================================================================= Date: Sat, 24 Sep 1994 23:40:53 -0400 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "Phillip A. Mitchem" Subject: Re: new relativity theor In-Reply-To: <9409250242.AA22651@gsusgi2.gsu.edu> On Sun, 25 Sep 1994, Glenda M Stocks wrote: > MM> I was wondering if the /3 applies to the exponent, the c^3, or > MM> the entire right side of the equation? > > the whole thing is /3. I sent it to you. He says to multiply e=mc^2 > by c/3 . Then you are saying that E=(MC^2)*(C/3)? That's a large difference. It would seem a difference of a factor of close to 100,000 would have shown up in experiments before now. You have perted my interest. Please continue. Phillip Mitchem email: usgpam@gsusgi2.gsu.edu Client Services Web Page: http://www.gsu.edu/dept/gsucc/cs/home.html Client Services Web Page on the Lan: http://enterprise.gsu.edu/index.htm Phillip's Home Page: http://gsusgi2.gsu.edu/~usgpam/phillip.html Some of my favorite quotes: Amicus usque ad aras. To Strive, to Seek, to Find and to never yield. I seem to be a verb. -B. Fuller ========================================================================= Date: Sun, 25 Sep 1994 23:46:02 -0400 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Grego10067 Organization: America Online, Inc. (1-800-827-6364) Subject: GEO-POD Construction System I am currently in the works with a manual I intend to publish soon, on the subject of Small scale Geodesic dome construction ( 8 to 22 ft Diameter ) I call them, GEO-PODs, I will include a method to quickly assemble a simplified version of the 3 frequency dome, and enable the reader to design their own dome with the formule that I supply in the manual, I will send the first 20 readers who respond to this message a free copy of my manual, Gratis, when it becomes complete in a few months. Simply send me an E-Mail message with your address and I will send you out a copy. Geodesicaly Yours Gregory D. Matherly GEO-POD construction systems ========================================================================= Date: Mon, 26 Sep 1994 08:23:09 CST Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "Larry W. Rhodes" Subject: Re: GEO-POD Construction System Date sent: Sun, 25 Sep 1994 23:46:02 -0400 Send reply to: List for the discussion of Buckminster Fuller's works From: Grego10067 Organization: America Online, Inc. (1-800-827-6364) Subject: GEO-POD Construction System To: Multiple recipients of list GEODESIC You wrote: I am currently in the works with a manual I intend to publish soon, on the subject of Small scale Geodesic dome construction ( 8 to 22 ft Diameter ) I call them, GEO-PODs, I will include a method to quickly assemble a simplified version of the 3 frequency dome, and enable the reader to design their own dome with the formule that I supply in the manual, I will send the first 20 readers who respond to this message a free copy of my manual, Gratis, when it becomes complete in a few months. Simply send me an E-Mail message with your address and I will send you out a copy. Geodesicaly Yours Gregory D. Matherly GEO-POD construction systems ********************************************************************** ********************************************************************** Plese send me a copy if I am within the limit. Live Long and Prosper, Larry W. RHodes lrhodes@chickasaw.astate.edu ========================================================================= Date: Mon, 26 Sep 1994 10:06:23 CST Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Tom Dosemagen Subject: Re: WANTED: Geodesic Dome Books Their regular phone number is 612-674-4292 and their fax number is 612-674-8561. ========================================================================= Date: Mon, 19 Sep 1994 02:31:00 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Tom Kukkee Organization: Norlink Information Service, Thunder Bay, Ont Canada Subject: NRG -"Global Challenge" 1/3 -------------------------------- Global NRG (Relativity) Challenge --------------------------------- Internet used as it should be is a world class facility with the ability to help solve the problems of the planet - in fact, it is a manifestation of the Universal Mind. I have seen the network's potential to debate and resolve difficult issues by utilizing knowledge and skill in a global forum. I respectfully request the help of each and everyone to test a hypothesis. I believe that I have found a simple, practical answer to the most sought after science issue ever - relativity. If my solution is not correct, it can go away. If it is true, we can all share in the benefits derived from it's eventual confirmation. The discovery is conceptually obtained by merely multiplying Albert Einstein's formula for energy E = M C ^ 2 by " C " yet one more time to "cube the speed of light" while dividing by 3 to adjust for the curvature of space and the effects of relativity. Virtually thousands of problems can be resolved from one physics statement: Gravity = M C ^ 3 / 3 (which is, of course, also 3 G = M C C C and G = E * C / 3). This discovery has resulted in a cascade of new knowledge and a vision of an exponential leap forward in all fields of science. It appears to set a new direction for research, promises "clean", "green" energy, and is intellectually satisfying in that -one- model of cosmology fits all. This solution produces the "Sacred Geometry" of Nature observable in geology, geophysics, meteorology, and astronomy. The research paper detailing this discovery is presently in -draft- form ( 110 pages double spaced ). It's contents indicate that considerable urgency is warranted. The abstract and conclusions (only) are contained in a separate posting following, plus details from the "NRG Research Centre". Unless specifically reserved, comments received may influence the finished paper, (with credit of course to the contributor). All comments are welcome, including all criticism. c 1994 - Tom Kukkee - all rights reserved - --------------------------------- NRG Research Centre tom.kukkee@norlink.com\ GEM*net BBS (807) 475-7010 ---------------------------------- G R A V I T Y I S M C ^ 3 / 3 Relativity Creates Nature's Sacred Geometry v10.0 September 10, 1994 A B S T R A C T Albert Einstein spent his last 30 years trying to find a single theoretical statement that would explain the behaviour of subatomic particles and the curved geometry of gravity ( ** National Geographic, May 1989, ppg 576 **). The solution is literally "cast in stone". "NRG (Energy) THEORY" considered the rotation of particles using the edges of energy planes as "guiding centres" in sequential "time slices". Relativistic acceleration changes the centre's order of symmetry of rotation and the volume traced, enabling force / space conversion. Sequential energy plane "slices" describe a complete, closed cosmological model of relativity. This study first reviews NRG Theory. It defines the environment for relativistic transformation, outlines the principles in physics that comprise the single unit NRG model, and details the geometric changes caused by acceleration. It then extends the model to multiplex the fractal assembly of matter. It cites combinations of the compound model's features that occur in Nature, thereby solving numerous present mysteries. The study develops the conclusion that Einstein's formula for energy E=MC^2 is one quadrant of one Euclidean "time slice" of a relativistic model that is not presently documented in science. The "Sacred Geometry" of natural structures and strong energy events in the Universe visibly demonstrate that Gravity = M C ^ 3 / 3. -------> many pages -------> VII) CONCLUSIONS Microwave energy creates the "Sacred Geometry" that is fundamental to Nature's structures. NRG modelling of the behaviour of microwave energy in natural particle accelerators reconciles disparate observable natural structures and events to one single physics model where no other viable explanations exist. Cosmologically, the NRG model is useful for solving abstract problems such as missing mass, the breaking of symmetry, and the very nature of "time". It supplies the missing "means" and "method of delivery" for Tectonic Strain Theory (TST) to interconnect physical phenomena to electromagnetism. The NRG model's fractal assembly of matter has been found physically "cast in stone". NRG Theory relativistically unifies the electromagnetic and gravitation phenomena into one cosmologic model of energy in a magnetohydrodynamic (MHD) environment through a force/space analogy using the ratio "Gravity : Energy = Volume : 4 * Area". The variables in the analogy can be synthesized to show that Einstein's Euclidean energy plane should be physically placed into the geometric solution to relativity illustrated by the NRG Model. ------------------------- NRG Theory correctly suggests that Einstein's energy formula E = M C ^ 2 should be extended to include gravity G = M C ^ 3 / 3. " GOD STILL DOES NOT PLAY DICE IN THE UNIVERSE " ------------------------- c 1994 - Tom Kukkee - all rights reserved - --------------------------------- NRG Research Centre tom.kukkee@norlink.com\ GEM*net BBS (807) 475-7010 ---------------------------------- N R G R E S E A R C H C E N T R E Updated September 12/94 NRG Research Centre Inc. is organizing as a non-profit corporation in response to the discovery of NRG. Nuclear Relativistic Gravitation is essentially the "cubing of light" according to the physics formula G = M C ^ 3 / 3. It's specific "fingerprint" has been identified as the driving force behind natural catastrophe's such as Hurricane Andrew, it is etched onto planetary surfaces, and it is responsible for the assembly of all matter. The Centre will be dedicated to the universal study, documentation, and dissemination of scientific knowledge evolving from the NRG discovery until the phenomenon is broadly accepted, applied, and integrated. The NRG Research Centre welcomes research associates who will contribute significantly to the Centre's efforts to - identify the most urgent implications of the NRG Effect, particularly in the areas of public safety and environment, and then advocate necessary response. - gather and cross reference interdisciplinary materials, applications, problems, conflicts, etc. - identify new opportunities to extend this knowledge Specifically, the Centre intends to: - generate self sustaining internal resources through scientific advancement of this issue - broaden awareness of NRG issues through development of educational materials, seminars, lectures - become a wide area access computer repository for photographs, computer programs, scientific papers, and documentation of occurrences and their implications. - actively seek and administer funds for specific research that leads to advances in the understanding and promotion of knowledge of harmonics in energy. The NRG effect may eclipse the most significant of scientific discoveries. It's relativistic characteristics interact with every aspect of scientific research, our health, environment, and public safety. Draft copies of the illustrated study are available for a $ 15.00 (U.S.) contribution to the centre, and $ 4.00 courrier fees. -Satifaction guaranteed- -Visa and M/C only- -------------------------------------- NRG RESEARCH CENTRE Internet Email tom.kukkee@norlink.com / GEM*net BBS (807) 475-7010 --------------------------------------- N R G R E S E A R C H C E N T R E ABOUT THE NRG DISCOVERY Revised August 1,1994 A 1991 discovery may unexpectedly solve numerous scientific problems. The phenomenon, temporarily called "nuclear resonant gravitation (NRG)", describes the behaviour of energy as it is accelerated relativistically. By simply multiplying Einstein's formula for energy, E = m c ^ 2 by c/3 to adjust for relativity, an interesting blueprint for cosmology is suggested. The NRG Model is constructed by combining existing science principles into one working model. Continued research over the last three years has shown that many combinations of the model's unique features are manifested in Nature. The "NRG Effect" is found in events such as glactic formations, hurricanes, crop circles, non-impact crater symmetry and rock structures. Repeated physical occurrences suggest that this "adventurous" extension of physics is the long overdue bridge between observation and theory. The concept seems viable in that the geometry and effects explain geophysical and other occurrences not presently understood. In addition, stone "artifacts" have been found that -appear- to conclusively support the discovery. The discoverer, Thomas C. Kukkee, and project advocates are seeking wide scientific opinion on this principle. A scientific paper exanding on NRG Theory and application is nearing completion. It will show the existence of a presently undocumented energy form which will extend physics exponentially, while posing a whole new set of questions for scientists. A discovery of this importance -must- be authenticated before public release to ensure fair access and adequate detail. Steps are being taken to obtain a learned evaluation and a fair dissemination. A call for a small group of volunteer professions to review the draft verion is expected soon, to be followed by a broad release. The NRG Research Centre is organizing as a none profit corporation to investigate, document, and advance this issue. The centre will serve as an interim repository for related files, papers, photographs, etc. until the issue is resolved in the scientific community. Wide area access is available by computer modem. Offers (unconditional) outlining support would be welcome. Mail Address : NRG Research Centre 605 Mohawk Cr. Thunder Bay, ON Canada P7C 5G4 Telephone (807) 475-3704 Internet E-mail To: tom.kukkee@norlink.com GEM*net BBS at: (807) 475-7010 : free log-on available as "Anonymous Caller", password "Guest" GLENDA STOCKS | FidoNet 1:330/201.0 SearchNet HeadQuarters | InterNet searchnet.zec@channel1.com Snet Mailing List info, SEND | BBS: 508-586-6977 / 617-961-4865 info snet-L TO | Download SEARCHNT.ZIP For Info! majordomo@world.std.com OR | Voicemail: +1-617-341-6114 subscribe snet-L "address" | FidoNet CHANNELS, & I_UFO moderator * RM 1.3 00257 * Reality is an illusion created by... you and I. ========================================================================= Date: Mon, 26 Sep 1994 16:40:00 -0400 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "H. Jeffrey Rosen" Subject: Re: GEO-POD Construction System You Wrote: I am currently in the works with a manual I intend to publish soon, on the subject of Small scale Geodesic dome construction ( 8 to 22 ft Diameter ) I call them, GEO-PODs, I will include a method to quickly assemble a simplified version of the 3 frequency dome, and enable the reader to design their own dome with the formule that I supply in the manual, I will send the first 20 readers who respond to this message a free copy of my manual, Gratis, when it becomes complete in a few months. Simply send me an E-Mail message with your address and I will send you out a copy. Geodesicaly Yours Gregory D. Matherly GEO-POD construction systems ************************************************************************ Please send a copy to: H.J. Rosen 2015 Autumn Chase Augusta, GA 30907 ========================================================================= Date: Mon, 26 Sep 1994 16:46:26 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: ADM_JHESS@VAX1.ACS.JMU.EDU Subject: Re: GEO-POD Construction System I would also like a copy. Thanks, Johlene Hess ========================================================================= Date: Mon, 26 Sep 1994 17:22:03 -0400 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Dome Fan Organization: America Online, Inc. (1-800-827-6364) Subject: Re: WANTED: Geodesic Dome Books The best resource I have found is from Timberline Geodesics: 2015 Blake Street Berkeley Ca 94704 1-800-DOME-HOME (800-366-3466) Ph: 510-849-4481 Fax: 510-849-3265 ========================================================================= Date: Mon, 26 Sep 1994 16:56:59 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "Robert L. Read" Organization: CS Dept, University of Texas at Austin Subject: Re: NRG -"Global Challenge" 1/3 The long post on NRG Theory is nonsense. I'll admit that there is a slim chance that it is correct, but that hypothesis is certainly not testable on the basis of text presented. I would suggest that nobody send any money to the NRG Corporation or whatever it is called until they have seen something from them that does not "quote" every fifth word. -- Robert L. Read, Member of the League for Programming Freedom ========================================================================= Date: Mon, 26 Sep 1994 19:31:58 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Karl Chwe Organization: Univ of Denver Law Library Subject: Re: NRG -"Global Challenge" 1/3 > The long post on NRG Theory is nonsense. I'll admit that there is > a slim chance that it is correct, but that hypothesis is certainly > not testable on the basis of text presented. I have nothing to add, except to say that the NRG theory really is nonsense. Complete, utter, pathetic nonsense. Everything in it, including the depiction of Einstein's achievements. ========================================================================= Date: Mon, 26 Sep 1994 22:47:44 -0600 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: CAPLATT@STTHOMAS.EDU Subject: subscribe I would like to subscribe ========================================================================= Date: Tue, 27 Sep 1994 13:45:45 CST Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Tom Dosemagen Subject: Re: GEO-POD Construction System Please send me one of your free manuals. Tom Dosemagen 7138 Schmidt Road Fort Atkinson, WI 53538 Thanx ========================================================================= Date: Tue, 27 Sep 1994 15:05:12 CST Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "Larry W. Rhodes" Subject: Re: NRG -"Global Challenge" 1/3 Concerning the NRG postings. They appear to be an attempt to "fool some of the people some of the time". Has anyone contacted Tom Kukkee directly? Maybe this is all a joke.Live Long and Prosper, Larry W. RHodes lrhodes@chickasaw.astate.edu ========================================================================= Date: Wed, 28 Sep 1994 01:13:35 -0500 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "Robert L. Read" Organization: CS Dept, University of Texas at Austin Subject: FElt analyis of a dome (LONG) Hi. This post gives a FElt file that corresponds to a 46 foot diameter geodesic dome made out of 4x4s, and includes the resulting output of FElt showing the force in each board. (I promised to do this about a month ago, during a discussion about whether or not geodesic domes can be analyzed via the stiffness method and computer programs. My position is that they can be.) I include a lot of details here that might not be interesting to everyone (or anyone?). 0) The dome is a 3-v "5/8" icosahedron Class 1, Method 1, icosahedron. That terminology is explained in the classic "Geodesic Math and How to Use It" by Kenner. In plain English, this is the most common residential style geodesic dome, sold by several companies, including Timberline Geodesics and Oregon Domes (I do not necessarily recommend or endorse either of those companies, but they seem to be market leaders). It DOES NOT use the trick discussed by Kenner to make a 5/8th dome sit perfectly flat on the ground (that is, the lowest nodes of the dome are not in a plane, and a very small amount of blocking would be required to make every lowest node rest flat on the ground.) 1) If you have the FElt package, you can use its very primitve object display features to see a top-down view of the dome. Personally, I use "Irit" for viewing my designs, a freeware solid modeller that is much nicer; if anyone has it, I'll send them the data file for this dome. 2) I am NOT a qualified structural engineer, although I do my homework. All my opinions on that subject are therefore humble, and in particular the statements made here should not be the basis for a judgement about when a dome would or would not fall down. 3) The FElt file uses data for pine 4x4s--roughly speaking. Wood is a wonderful but heterogenous material, its properties differing from species to species and the number of knotholes in it etc. The numbers I use are estimates I get from books, but I don't know if they really are right for what you buy at the local hardware store. 4) The current FElt file applies a load downward of 2000 lbs at each of the 65 nodes. (15 of these are considered by FElt to be supported by the ground, so don't really count structurally.) Thus the current file applies an evenly distributed downward load of 80,000 pounds. The structural wood in the structure would weigh about 5,000 lbs, and cost about $2000. Note, however, that this is JUST a skeleton, not the blocking and plywood sheathing that have to be added to practical domes. 5) I use the Meter-Newton-Pascal system of units. The "Pascal" is a unit of stress, like Pounds per Square Inch or psi. The result of the running FElt on my input file is an output file which shows the tension or compression in every member in terms of Pascals. According to a book by Buchanan, the "allowable stress" in pine in compression parallel to the grain is 5.5 MegaPascals, or 5.5 million Pascals. The loading given for the design given generates no more than 4 million Pascals in any member, which I take to mean that it is a safe design for that particular loading. (Note: I have seen one reference that suggest that the tensional capacity of wood parallel to the grain is generally greater than the compressional capacity, but have not seen this repeated or even mentioned anywhere else. Apparently, the tensional strength of wood is hard to measure.) 6) This suggest an impressive load-bearing capacity for the amount of wood used. However, the FElt program's analysis is limited in many ways that must be understood if people's lives are going to depend on anything you build: A) The program is assuming that the joints are stronger than the members. This might be hard to ensure in practice, and would depend on a well-designed joining mechanism. B) The particular files given test only one particular loading; in particular, no lateral wind load is assumed. Although such things can be easily analyzed by FElt by modifying the input file, a designer must try to imagine all possible situations, and running all possible situations through FElt would take a long time (:->). C) There could be a bug in FElt. D) A given load, such as a load of wet snow, would press on each member, potentially snapping them locally. The current input file to FElt assumes all load are applied to the node points themselves, which is not really physically realistic. E) Some assumption of mine could be wrong. F) I have made all joint constraints "free", which is modelling the physical situation of universal joints at each connection allowing perfect freedom of movement angularly. This is not realistic for most domes, which have joints that are just nailed together or maybe use metal brackets. However, this is justified by the omni-triangulated aspect of a dome -- you can't change the angles of a triangle made out of 4x4s very much without shattering one of the boards, and so the system breaks before the angle can change enough to modify the geometry significantly enough to change how force gets distributed. G) When a structural member is under compression, it has too be fat enough that it will be "crushed" before it will "buckle", like a column. Books like "Mechanics of Materials" by Buchanan give formulae for determining if a structure member must be treated as a column or as a compressive member. In some cases, such as the case where the triangles of the dome will be "blocked" with studs that run from the middle parts of one member to the middle parts of another, these members prevent buckling and column-wise failure need not be considered. The members in this design are about 10 feet long, and, with a minimum diameter of 3.5 inches since we use 4x4s, the sigma_allow for the members as long columns is greater than the sigma_allow for compression, so it's not a problem. 7) Even though all those caveats must be observed, I think FElt, or something like it, is a fundamentally valuable tool to geodesic/synergistic/Fullerite designer. It certainly has given me confidence. 8) It would WONDERFUL if someone would input a simple house-like rectillinear style structure so that we could use FElt to compare a dome to "normal" house in a scientific manner. But be forewarned -- this is not as easy as it looks, since you'll have to worry some about joint constraints. The following file a "problem" for FElt -- the geometry of the dome structure, the connections between nodes, and loading. It won't be too sensible if you don't know about FElt. Remember the system of units if Newton-Meter-Pascal, so the roof apex (node 32) is 6.75 meters off the ground, or 23 feet. File #1: The FElt input file <<< Cut right below this line>> problem description title="Rob Read's 5/8 3-v icosa dome w/o base flattening " nodes = 61 elements = 165 constraints ground tx = c ty = c tz = c free tx = u ty = u tz = u slider tx = u ty = u tz = c nodes 1 x = 0 y = 0 z = 7.0104 constraint = free force = person 2 x = -5.96341 y = 1.93763 z = 3.13514 constraint = free force = person 3 x = 0 y = 6.2703 z = 3.13514 constraint = free force = person 4 x = 0 y = 2.40652 z = 6.5844 constraint = free force = person 5 x = -2.28874 y = 0.743655 z = 6.5844 constraint = free force = person 6 x = 0 y = 4.81304 z = 5.09709 constraint = free force = person 7 x = -4.57748 y = 1.48731 z = 5.09709 constraint = free force = person 8 x = -2.50147 y = 3.44297 z = 5.57084 constraint = free force = person 9 x = -4.57748 y = 3.89383 z = 3.60977 constraint = free force = person 10 x = -2.28874 y = 5.5567 z = 3.60977 constraint = free force = person 11 x = 5.96341 y = 1.93763 z = 3.13514 constraint = free force = person 12 x = 2.28874 y = 0.743655 z = 6.5844 constraint = free force = person 13 x = 4.57748 y = 1.48731 z = 5.09709 constraint = free force = person 14 x = 2.50147 y = 3.44297 z = 5.57084 constraint = free force = person 15 x = 2.28874 y = 5.5567 z = 3.60977 constraint = free force = person 16 x = 4.57748 y = 3.89383 z = 3.60977 constraint = free force = person 17 x = 3.68559 y = -5.07278 z = 3.13514 constraint = free force = person 18 x = 1.41452 y = -1.94692 z = 6.5844 constraint = free force = person 19 x = 2.82904 y = -3.89383 z = 5.09709 constraint = free force = person 20 x = 4.04746 y = -1.3151 z = 5.57084 constraint = free force = person 21 x = 5.99199 y = -0.459605 z = 3.60978 constraint = free force = person 22 x = 5.11777 y = -3.15018 z = 3.60977 constraint = free force = person 23 x = -3.68559 y = -5.07278 z = 3.13514 constraint = free force = person 24 x = -1.41452 y = -1.94692 z = 6.5844 constraint = free force = person 25 x = -2.82904 y = -3.89383 z = 5.09709 constraint = free force = person 26 x = 0 y = -4.25575 z = 5.57084 constraint = free force = person 27 x = 1.41452 y = -5.84075 z = 3.60978 constraint = free force = person 28 x = -1.41452 y = -5.84075 z = 3.60978 constraint = free force = person 29 x = -4.04746 y = -1.3151 z = 5.57084 constraint = free force = person 30 x = -5.11777 y = -3.15018 z = 3.60977 constraint = free force = person 31 x = -5.99199 y = -0.459605 z = 3.60978 constraint = free force = person 32 x = 1.41452 y = 6.75996 z = 1.20326 constraint = free force = person 33 x = 2.82903 y = 6.30035 z = -1.20326 constraint = ground force = person 34 x = 4.04746 y = 5.57085 z = 1.3151 constraint = free force = person 35 x = 5.99199 y = 3.43423 z = 1.20326 constraint = free force = person 36 x = 5.11777 y = 4.63749 z = -1.20326 constraint = slider force = person 37 x = 6.86621 y = 0.743656 z = 1.20326 constraint = free force = person 38 x = 6.86621 y = -0.743656 z = -1.20326 constraint = slider force = person 39 x = 6.54892 y = -2.12787 z = 1.3151 constraint = free force = person 40 x = 5.11777 y = -4.63749 z = 1.20326 constraint = free force = person 41 x = 5.99199 y = -3.43423 z = -1.20326 constraint = slider force = person 42 x = 2.82903 y = -6.30035 z = 1.20326 constraint = free force = person 43 x = 1.41452 y = -6.75996 z = -1.20326 constraint = slider force = person 44 x = 0 y = -6.88594 z = 1.3151 constraint = free force = person 45 x = -2.82903 y = -6.30035 z = 1.20326 constraint = free force = person 46 x = -1.41452 y = -6.75996 z = -1.20326 constraint = slider force = person 47 x = -5.11777 y = -4.63749 z = 1.20326 constraint = free force = person 48 x = -5.99199 y = -3.43423 z = -1.20326 constraint = slider force = person 49 x = -6.54892 y = -2.12787 z = 1.3151 constraint = free force = person 50 x = -6.86621 y = 0.743656 z = 1.20326 constraint = free force = person 51 x = -6.86621 y = -0.743656 z = -1.20326 constraint = slider force = person 52 x = -1.41452 y = 6.75996 z = 1.20326 constraint = free force = person 53 x = -2.82903 y = 6.30035 z = -1.20326 constraint = slider force = person 54 x = -4.04746 y = 5.57085 z = 1.3151 constraint = free force = person 55 x = -5.99199 y = 3.43423 z = 1.20326 constraint = free force = person 56 x = -5.11777 y = 4.63749 z = -1.20326 constraint = slider force = person 57 x = 0 y = 6.88594 z = -1.3151 constraint = slider force = person 58 x = 6.54892 y = 2.12787 z = -1.3151 constraint = slider force = person 59 x = 4.04746 y = -5.57085 z = -1.3151 constraint = slider force = person 60 x = -4.04746 y = -5.57085 z = -1.3151 constraint = slider force = person 61 x = -6.54892 y = 2.12787 z = -1.3151 constraint = slider force = person truss elements 1 nodes = [1 5] material = WolmanizedFourxFour 2 nodes = [1 4] material = WolmanizedFourxFour 3 nodes = [5 4] material = WolmanizedFourxFour 4 nodes = [5 7] material = WolmanizedFourxFour 5 nodes = [5 8] material = WolmanizedFourxFour 6 nodes = [7 8] material = WolmanizedFourxFour 7 nodes = [4 8] material = WolmanizedFourxFour 8 nodes = [4 6] material = WolmanizedFourxFour 9 nodes = [8 6] material = WolmanizedFourxFour 10 nodes = [7 2] material = WolmanizedFourxFour 11 nodes = [7 9] material = WolmanizedFourxFour 12 nodes = [2 9] material = WolmanizedFourxFour 13 nodes = [8 9] material = WolmanizedFourxFour 14 nodes = [8 10] material = WolmanizedFourxFour 15 nodes = [9 10] material = WolmanizedFourxFour 16 nodes = [6 10] material = WolmanizedFourxFour 17 nodes = [6 3] material = WolmanizedFourxFour 18 nodes = [10 3] material = WolmanizedFourxFour 19 nodes = [1 12] material = WolmanizedFourxFour 20 nodes = [4 12] material = WolmanizedFourxFour 21 nodes = [4 14] material = WolmanizedFourxFour 22 nodes = [6 14] material = WolmanizedFourxFour 23 nodes = [12 14] material = WolmanizedFourxFour 24 nodes = [12 13] material = WolmanizedFourxFour 25 nodes = [14 13] material = WolmanizedFourxFour 26 nodes = [6 15] material = WolmanizedFourxFour 27 nodes = [3 15] material = WolmanizedFourxFour 28 nodes = [14 15] material = WolmanizedFourxFour 29 nodes = [14 16] material = WolmanizedFourxFour 30 nodes = [15 16] material = WolmanizedFourxFour 31 nodes = [13 16] material = WolmanizedFourxFour 32 nodes = [13 11] material = WolmanizedFourxFour 33 nodes = [16 11] material = WolmanizedFourxFour 34 nodes = [1 18] material = WolmanizedFourxFour 35 nodes = [12 18] material = WolmanizedFourxFour 36 nodes = [12 20] material = WolmanizedFourxFour 37 nodes = [13 20] material = WolmanizedFourxFour 38 nodes = [18 20] material = WolmanizedFourxFour 39 nodes = [18 19] material = WolmanizedFourxFour 40 nodes = [20 19] material = WolmanizedFourxFour 41 nodes = [13 21] material = WolmanizedFourxFour 42 nodes = [11 21] material = WolmanizedFourxFour 43 nodes = [20 21] material = WolmanizedFourxFour 44 nodes = [20 22] material = WolmanizedFourxFour 45 nodes = [21 22] material = WolmanizedFourxFour 46 nodes = [19 22] material = WolmanizedFourxFour 47 nodes = [19 17] material = WolmanizedFourxFour 48 nodes = [22 17] material = WolmanizedFourxFour 49 nodes = [1 24] material = WolmanizedFourxFour 50 nodes = [18 24] material = WolmanizedFourxFour 51 nodes = [18 26] material = WolmanizedFourxFour 52 nodes = [19 26] material = WolmanizedFourxFour 53 nodes = [24 26] material = WolmanizedFourxFour 54 nodes = [24 25] material = WolmanizedFourxFour 55 nodes = [26 25] material = WolmanizedFourxFour 56 nodes = [19 27] material = WolmanizedFourxFour 57 nodes = [17 27] material = WolmanizedFourxFour 58 nodes = [26 27] material = WolmanizedFourxFour 59 nodes = [26 28] material = WolmanizedFourxFour 60 nodes = [27 28] material = WolmanizedFourxFour 61 nodes = [25 28] material = WolmanizedFourxFour 62 nodes = [25 23] material = WolmanizedFourxFour 63 nodes = [28 23] material = WolmanizedFourxFour 64 nodes = [24 5] material = WolmanizedFourxFour 65 nodes = [24 29] material = WolmanizedFourxFour 66 nodes = [25 29] material = WolmanizedFourxFour 67 nodes = [5 29] material = WolmanizedFourxFour 68 nodes = [29 7] material = WolmanizedFourxFour 69 nodes = [25 30] material = WolmanizedFourxFour 70 nodes = [23 30] material = WolmanizedFourxFour 71 nodes = [29 30] material = WolmanizedFourxFour 72 nodes = [29 31] material = WolmanizedFourxFour 73 nodes = [30 31] material = WolmanizedFourxFour 74 nodes = [7 31] material = WolmanizedFourxFour 75 nodes = [31 2] material = WolmanizedFourxFour 76 nodes = [3 32] material = WolmanizedFourxFour 77 nodes = [15 32] material = WolmanizedFourxFour 78 nodes = [15 34] material = WolmanizedFourxFour 79 nodes = [16 34] material = WolmanizedFourxFour 80 nodes = [32 34] material = WolmanizedFourxFour 81 nodes = [32 33] material = WolmanizedFourxFour 82 nodes = [34 33] material = WolmanizedFourxFour 83 nodes = [16 35] material = WolmanizedFourxFour 84 nodes = [11 35] material = WolmanizedFourxFour 85 nodes = [34 35] material = WolmanizedFourxFour 86 nodes = [34 36] material = WolmanizedFourxFour 87 nodes = [35 36] material = WolmanizedFourxFour 88 nodes = [33 36] material = WolmanizedFourxFour 89 nodes = [11 37] material = WolmanizedFourxFour 90 nodes = [21 37] material = WolmanizedFourxFour 91 nodes = [21 39] material = WolmanizedFourxFour 92 nodes = [22 39] material = WolmanizedFourxFour 93 nodes = [37 39] material = WolmanizedFourxFour 94 nodes = [37 38] material = WolmanizedFourxFour 95 nodes = [39 38] material = WolmanizedFourxFour 96 nodes = [22 40] material = WolmanizedFourxFour 97 nodes = [17 40] material = WolmanizedFourxFour 98 nodes = [39 40] material = WolmanizedFourxFour 99 nodes = [39 41] material = WolmanizedFourxFour 100 nodes = [40 41] material = WolmanizedFourxFour 101 nodes = [38 41] material = WolmanizedFourxFour 102 nodes = [17 42] material = WolmanizedFourxFour 103 nodes = [27 42] material = WolmanizedFourxFour 104 nodes = [27 44] material = WolmanizedFourxFour 105 nodes = [28 44] material = WolmanizedFourxFour 106 nodes = [42 44] material = WolmanizedFourxFour 107 nodes = [42 43] material = WolmanizedFourxFour 108 nodes = [44 43] material = WolmanizedFourxFour 109 nodes = [28 45] material = WolmanizedFourxFour 110 nodes = [23 45] material = WolmanizedFourxFour 111 nodes = [44 45] material = WolmanizedFourxFour 112 nodes = [44 46] material = WolmanizedFourxFour 113 nodes = [45 46] material = WolmanizedFourxFour 114 nodes = [43 46] material = WolmanizedFourxFour 115 nodes = [23 47] material = WolmanizedFourxFour 116 nodes = [30 47] material = WolmanizedFourxFour 117 nodes = [30 49] material = WolmanizedFourxFour 118 nodes = [31 49] material = WolmanizedFourxFour 119 nodes = [47 49] material = WolmanizedFourxFour 120 nodes = [47 48] material = WolmanizedFourxFour 121 nodes = [49 48] material = WolmanizedFourxFour 122 nodes = [31 50] material = WolmanizedFourxFour 123 nodes = [2 50] material = WolmanizedFourxFour 124 nodes = [49 50] material = WolmanizedFourxFour 125 nodes = [49 51] material = WolmanizedFourxFour 126 nodes = [50 51] material = WolmanizedFourxFour 127 nodes = [48 51] material = WolmanizedFourxFour 128 nodes = [3 52] material = WolmanizedFourxFour 129 nodes = [10 52] material = WolmanizedFourxFour 130 nodes = [10 54] material = WolmanizedFourxFour 131 nodes = [9 54] material = WolmanizedFourxFour 132 nodes = [52 54] material = WolmanizedFourxFour 133 nodes = [52 53] material = WolmanizedFourxFour 134 nodes = [54 53] material = WolmanizedFourxFour 135 nodes = [9 55] material = WolmanizedFourxFour 136 nodes = [2 55] material = WolmanizedFourxFour 137 nodes = [54 55] material = WolmanizedFourxFour 138 nodes = [54 56] material = WolmanizedFourxFour 139 nodes = [55 56] material = WolmanizedFourxFour 140 nodes = [53 56] material = WolmanizedFourxFour 141 nodes = [53 57] material = WolmanizedFourxFour 142 nodes = [57 52] material = WolmanizedFourxFour 143 nodes = [57 33] material = WolmanizedFourxFour 144 nodes = [57 32] material = WolmanizedFourxFour 145 nodes = [52 32] material = WolmanizedFourxFour 146 nodes = [36 58] material = WolmanizedFourxFour 147 nodes = [58 35] material = WolmanizedFourxFour 148 nodes = [58 38] material = WolmanizedFourxFour 149 nodes = [58 37] material = WolmanizedFourxFour 150 nodes = [35 37] material = WolmanizedFourxFour 151 nodes = [41 59] material = WolmanizedFourxFour 152 nodes = [59 40] material = WolmanizedFourxFour 153 nodes = [59 43] material = WolmanizedFourxFour 154 nodes = [59 42] material = WolmanizedFourxFour 155 nodes = [40 42] material = WolmanizedFourxFour 156 nodes = [46 60] material = WolmanizedFourxFour 157 nodes = [60 45] material = WolmanizedFourxFour 158 nodes = [60 48] material = WolmanizedFourxFour 159 nodes = [60 47] material = WolmanizedFourxFour 160 nodes = [45 47] material = WolmanizedFourxFour 161 nodes = [51 61] material = WolmanizedFourxFour 162 nodes = [61 50] material = WolmanizedFourxFour 163 nodes = [61 56] material = WolmanizedFourxFour 164 nodes = [61 55] material = WolmanizedFourxFour 165 nodes = [50 55] material = WolmanizedFourxFour material properties WolmanizedFourxFour E=10e+9 A=0.00790321 No1PineTwoxFour E=10e+9 A=0.00338709 No1PineTwoxSix E=10e+9 A=0.00532257 forces person Fz = -8896.44 post Fz = 0 wind Fx = 13344.7 Fz = -1270.92 chand Fz = -1270.92 end <<< Cut right above this line>> <<< Cut right below this line>> ** Rob Read's 5/8 3-v icosa dome w/o base flattening ** Nodal Displacements ----------------------------------------------------------------------------- Node # DOF 1 DOF 2 DOF 3 DOF 4 DOF 5 DOF 6 ----------------------------------------------------------------------------- 1 -0.00028197 -0.0010033 -0.0050426 0 0 0 2 -0.00086141 -0.0010953 -0.001948 0 0 0 3 -0.00054853 -0.00048064 -0.001948 0 0 0 4 -0.00038427 -0.0011182 -0.0038811 0 0 0 5 -0.00020425 -0.0011361 -0.0038811 0 0 0 6 -0.00048658 -0.00095828 -0.0028452 0 0 0 7 -0.000388 -0.001184 -0.0028452 0 0 0 8 -0.00041951 -0.0011218 -0.0031018 0 0 0 9 -0.00092711 -0.00078612 -0.0019558 0 0 0 10 -0.00076159 -0.00051721 -0.0019558 0 0 0 11 0.00013273 -0.00058826 -0.001948 0 0 0 12 -0.00042292 -0.0009415 -0.0038811 0 0 0 13 -0.0003024 -0.00079478 -0.0028452 0 0 0 14 -0.00043716 -0.00090908 -0.0031018 0 0 0 15 -0.0002748 -0.00032261 -0.0019558 0 0 0 16 3.2106e-05 -0.00039693 -0.0019558 0 0 0 17 0.00024089 -0.0012694 -0.0019479 0 0 0 18 -0.00026677 -0.00085014 -0.0038811 0 0 0 19 -8.9987e-05 -0.00091941 -0.0028452 0 0 0 20 -0.00024034 -0.00082657 -0.0031018 0 0 0 21 0.0003676 -0.00079976 -0.0019558 0 0 0 22 0.00039176 -0.0011146 -0.0019558 0 0 0 23 -0.00037353 -0.0015828 -0.0019479 0 0 0 24 -0.00013163 -0.00097041 -0.0038811 0 0 0 25 -0.00014289 -0.0011599 -0.0028452 0 0 0 26 -0.00010105 -0.00098826 -0.0031018 0 0 0 27 0.00011232 -0.0015582 -0.0019558 0 0 0 28 -0.00017966 -0.0016784 -0.0019558 0 0 0 29 -0.00021179 -0.0011707 -0.0031018 0 0 0 30 -0.00068786 -0.0015497 -0.0019558 0 0 0 31 -0.00089247 -0.0013092 -0.0019558 0 0 0 32 -0.00013451 0.0009538 -0.00084626 0 0 0 33 0 0 0 0 0 0 34 0.00067431 0.00081094 -0.0007434 0 0 0 35 0.0012418 0.00025118 -0.00084625 0 0 0 36 0.00019086 1.0092e-05 0 0 0 0 37 0.0016249 -0.00053875 -0.00084625 0 0 0 38 0.00075944 -0.00096142 0 0 0 0 39 0.001739 -0.0013521 -0.0007434 0 0 0 40 0.0013819 -0.0020648 -0.00084625 0 0 0 41 0.00082778 -0.0011397 0 0 0 0 42 0.00074907 -0.0026732 -0.00084624 0 0 0 43 7.965e-05 -0.0019807 0 0 0 0 44 1.0763e-05 -0.0030331 -0.0007434 0 0 0 45 -0.00077734 -0.0029138 -0.00084624 0 0 0 46 -6.8836e-05 -0.002101 0 0 0 0 47 -0.0015516 -0.0024999 -0.00084625 0 0 0 48 -0.0010997 -0.0016492 0 0 0 0 49 -0.002122 -0.0019089 -0.0007434 0 0 0 50 -0.002252 -0.0011225 -0.00084625 0 0 0 51 -0.0012602 -0.0015452 0 0 0 0 52 -0.0010042 0.00083354 -0.00084626 0 0 0 53 -0.0010996 -0.00024053 0 0 0 0 54 -0.0017119 0.00046682 -0.0007434 0 0 0 55 -0.0020977 -0.00025828 -0.00084625 0 0 0 56 -0.0011491 -0.00042504 0 0 0 0 57 -0.0005747 -0.0020817 0 0 0 0 58 -0.0013981 -0.0010581 0 0 0 0 59 -0.00067891 4.1071e-05 0 0 0 0 60 0.00058862 -0.00030306 0 0 0 0 61 0.00065326 -0.001615 0 0 0 0 Element Stresses ------------------------------------------------------------------------------- 1: -1.2916e+06 2: -1.2916e+06 3: -4.7769e+05 4: -1.444e+06 5: -8.4381e+05 6: -78190 7: -8.438e+05 8: -1.4441e+06 9: -78193 10: -1.7818e+06 11: -4.5655e+05 12: 8.539e+05 13: -1.247e+06 14: -1.247e+06 15: 1.0321e+06 16: -4.5656e+05 17: -1.7818e+06 18: 8.539e+05 19: -1.2916e+06 20: -4.7769e+05 21: -8.438e+05 22: -78193 23: -8.4381e+05 24: -1.444e+06 25: -78190 26: -4.5656e+05 27: 8.539e+05 28: -1.247e+06 29: -1.247e+06 30: 1.0321e+06 31: -4.5655e+05 32: -1.7818e+06 33: 8.539e+05 34: -1.2916e+06 35: -4.7769e+05 36: -8.4381e+05 37: -78190 38: -8.438e+05 39: -1.4441e+06 40: -78194 41: -4.5655e+05 42: 8.5391e+05 43: -1.247e+06 44: -1.247e+06 45: 1.0321e+06 46: -4.5656e+05 47: -1.7819e+06 48: 8.5391e+05 49: -1.2916e+06 50: -4.7769e+05 51: -8.4381e+05 52: -78199 53: -8.4381e+05 54: -1.4441e+06 55: -78199 56: -4.5654e+05 57: 8.5391e+05 58: -1.247e+06 59: -1.247e+06 60: 1.0321e+06 61: -4.5654e+05 62: -1.7819e+06 63: 8.5391e+05 64: -4.7769e+05 65: -8.438e+05 66: -78194 67: -8.4381e+05 68: -78190 69: -4.5656e+05 70: 8.5391e+05 71: -1.247e+06 72: -1.247e+06 73: 1.0321e+06 74: -4.5655e+05 75: 8.5391e+05 76: -1.407e+06 77: -1.5705e+06 78: -1.3122e+06 79: -1.3121e+06 80: 2.7647e+06 81: -1.7591e+06 82: -1.9646e+06 83: -1.5705e+06 84: -1.407e+06 85: 2.7647e+06 86: -1.9645e+06 87: -1.7591e+06 88: 5.2482e+05 89: -1.407e+06 90: -1.5705e+06 91: -1.3122e+06 92: -1.3121e+06 93: 2.7647e+06 94: -1.7591e+06 95: -1.9645e+06 96: -1.5705e+06 97: -1.407e+06 98: 2.7647e+06 99: -1.9645e+06 100: -1.7591e+06 101: 5.2484e+05 102: -1.407e+06 103: -1.5705e+06 104: -1.3121e+06 105: -1.3121e+06 106: 2.7646e+06 107: -1.7591e+06 108: -1.9645e+06 109: -1.5705e+06 110: -1.407e+06 111: 2.7646e+06 112: -1.9645e+06 113: -1.7591e+06 114: 5.2486e+05 115: -1.407e+06 116: -1.5705e+06 117: -1.3121e+06 118: -1.3122e+06 119: 2.7647e+06 120: -1.7591e+06 121: -1.9645e+06 122: -1.5705e+06 123: -1.407e+06 124: 2.7647e+06 125: -1.9645e+06 126: -1.7591e+06 127: 5.2484e+05 128: -1.407e+06 129: -1.5705e+06 130: -1.3122e+06 131: -1.3121e+06 132: 2.7647e+06 133: -1.7591e+06 134: -1.9646e+06 135: -1.5705e+06 136: -1.407e+06 137: 2.7647e+06 138: -1.9645e+06 139: -1.7591e+06 140: 5.2482e+05 141: 4.8667e+05 142: -2.2622e+06 143: 4.8667e+05 144: -2.2622e+06 145: 3.0741e+06 146: 4.8669e+05 147: -2.2622e+06 148: 4.867e+05 149: -2.2622e+06 150: 3.074e+06 151: 4.8672e+05 152: -2.2622e+06 153: 4.8673e+05 154: -2.2622e+06 155: 3.074e+06 156: 4.8673e+05 157: -2.2622e+06 158: 4.8672e+05 159: -2.2622e+06 160: 3.074e+06 161: 4.867e+05 162: -2.2622e+06 163: 4.8669e+05 164: -2.2622e+06 165: 3.074e+06 Reaction Forces ----------------------------------- Node # DOF Reaction Force ----------------------------------- 33 Tx -8.0512e-11 33 Ty 1.7617e-11 33 Tz 25499 36 Tz 25499 38 Tz 25499 41 Tz 25499 43 Tz 25499 46 Tz 25499 48 Tz 25499 51 Tz 25499 53 Tz 25499 56 Tz 25499 57 Tz 30849 58 Tz 30849 59 Tz 30849 60 Tz 30849 61 Tz 30849 <<< Cut right above this line>> -- Robert L. Read, Member of the League for Programming Freedom ========================================================================= Date: Wed, 28 Sep 1994 10:50:04 -0400 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Grego10067 Organization: America Online, Inc. (1-800-827-6364) Subject: FREE MANUAL You are one of the last ones to get a free manual, it will arrive in about two months after writing, and printing are complete. Sincerely, GEO-POD Systems ========================================================================= Date: Wed, 28 Sep 1994 15:26:55 GMT Reply-To: bcarroll@Eng.Sun.COM Sender: List for the discussion of Buckminster Fuller's works From: Bruce Carroll - Sun BOS Systems Product Assurance CONTRACTOR Organization: Sun Microsystems Inc. - BDC Subject: Re: WANTED: Geodesic Dome Books I had some request to convert my Windows cardfile of 17 entries of Dome manufactures (and one book) into ASCII, so here it is below. Enjoy. Bruce Carroll -------------------------------------------------- American Ingenuity 3500-B Harlock Rd., Melbourne, FL 32934 407-254-4220 $8 for planning kit EPS Foam covered w/concrete Shells -------------------------------------------------- Cascade Domes P.O. Box 1977 Florence, OR 97439 Dome Kits, Aluminum frames $12 for catalog -------------------------------------------------- Domes America 6345 W. Jolie Rd. Countryside, IL 60525 708-579-9400 -------------------------------------------------- DomEstic Designs P.O. Box 4203 Bellevue, Wa 98009 -------------------------------------------------- Geodesic Domes & Homes 608 Hwy. 110 N. Whitehouse, TX 75791 903-839-2000 -------------------------------------------------- GeoDomes Woodworks 6876 Indiana, RM-10 Riverside, CA 92506 909-787-8800 $15 for catalog Wood kits -------------------------------------------------- Key Dome P.O. Box 430253 Miami, FL 33143 305-665-3541 - voice 305-667-1256 - fax Peter Vanderklaaw Dome plans/blueprints (from $54 to $200) All plywood, plywood panels & EPS foam w/concrete shell -------------------------------------------------- KingDomes P.O. Box 980427 Houston, TX 77098 Send $2-5 for info. European design, 163 solutions, kits, math. -------------------------------------------------- Monolithic Constructors, Inc. P.O. Box 479 Italy, TX 76651 800-608-0001 $19.95 video brochure Concrete monolithic Domes -------------------------------------------------- Natural Space Domes 37955 Bridge Road, North Branch MN 55056 800-733-7107 -------------------------------------------------- Oregon Dome, Inc. 3215 Meadow Lane Eugene, OR 97402 503-689-3443 $12 for catalog -------------------------------------------------- Precision Structures 2566 Potter St. Eugene, OR 97405 $34.95 for book "Professional Dome Plans" See Mother Earth News Jan. 1990 for review -------------------------------------------------- Semispheres 1505 Webster St. Richmond, VA 23220 804-643-3184 ugly looking! -------------------------------------------------- Shelter Systems P.O. Box 1294 Capitola, CA 95010 Send $1 for info. Large dome tents, etc. -------------------------------------------------- Stromberg's Chicks & Gamebirds P.O. Box 400 Pine River, 4, MN 56474 218-587-2222 $39.95 for Starplate struts to build a dome shed/greenhouse up to 14ft in diameter.They mostly sell chicks and supplies, but have these starplates for making sheds -------------------------------------------------- Timberline Geodesics 2015 Blake St. Berkeley, CA 94704 800-DOME-HOME $12 for catalog -------------------------------------------------- Topsider Homes P.O. Box 848 Yadkinville, NC 27055 910-766-9300 round homes, not domes -------------------------------------------------- ========================================================================= Date: Wed, 28 Sep 1994 19:08:31 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Murray Brain Calvert Organization: Brock University, St. Catharines Ontario Subject: Re: new relativity theor Phillip A. Mitchem (usgpam@GSUSGI2.GSU.EDU) wrote: : On Sun, 25 Sep 1994, Glenda M Stocks wrote: : > MM> I was wondering if the /3 applies to the exponent, the c^3, or : > MM> the entire right side of the equation? : > : > the whole thing is /3. I sent it to you. He says to multiply e=mc^2 : > by c/3 . : Then you are saying that E=(MC^2)*(C/3)? That's a large difference. : It would seem a difference of a factor of close to 100,000 would have : shown up in experiments before now. You have perted my interest. Please : continue. It also brings in the UNITS "Metres per second", which makes the formula produce a quantity which could not possibly be energy. All formulas in Physics must not depend on the units of length, mass and time which are arbitrary conventions. See the subject "Dimensional Analysis". Brian Calvert ========================================================================= Date: Wed, 28 Sep 1994 16:36:06 -0400 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Grego10067 Organization: America Online, Inc. (1-800-827-6364) Subject: GEO-POD UPDATE !!!!!!!!!!!!!!!!!!!!!!! Thank you for the great response to my free book offer, I have received E-Mail from as far away north as the Netherlands, and as far south as Sao Paulo, Brazil. I had to cut off the free offer as I had over 100 inquirys in 1 day. I will honor the 100 that I have received so far. but no more free books after Sept-28th- 0600Hrs. If you would like to obtain a GEO-POD Systems construction manual, you may still send your request, and it will be held for you. The actual price will not be known untill after printing, but it most likely will be about $5.00 Sincerely, GEO-POD Systems ========================================================================= Date: Fri, 30 Sep 1994 21:20:42 EDT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: SGoddard@AOL.COM Subject: I'm curious I teach 6th grade and I want to have my students construct geodesic domes to sleep in. Where should I go for easy to follow directions/plans? Roberto Lovato c/o S Goddard