From <@UBVM.CC.BUFFALO.EDU:owner-LISTSERV@UBVM.CC.BUFFALO.EDU> Mon Feb 6 16:04:58 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 QAA27271 for ; Mon, 6 Feb 1995 16:04:58 -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 QAA01829 for ; Mon, 6 Feb 1995 16:04:44 -0500 Message-Id: <199502062104.QAA01829@netaxs.com> Received: from UBVM.CC.BUFFALO.EDU by UBVM.cc.buffalo.edu (IBM VM SMTP V2R2) with BSMTP id 4118; Mon, 06 Feb 95 16:03:42 EST Received: from UBVM.CC.BUFFALO.EDU (NJE origin LISTSERV@UBVM) by UBVM.CC.BUFFALO.EDU (LMail V1.2a/1.8a) with BSMTP id 9077; Mon, 6 Feb 1995 12:40:15 -0500 Date: Mon, 6 Feb 1995 12:39:52 -0500 From: "L-Soft list server at UBVM (1.8a)" Subject: File: "GEODESIC LOG9408" To: "Christopher J. Fearnley" Status: RO ========================================================================= Date: Mon, 1 Aug 1994 08:34:27 +0100 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Andy Wardley Subject: Re: LOOKING FOR SYNERGETICS II In-Reply-To: <9407311749.AA01178@Q.icl.co.uk> from "The Butterfly" at Jul 31, 94 03:45:14 pm The Butterfly writes: > Oh, and I saw that GEODOME.JPG file. VERY impressive! Nice Ray-trace, >Andy! (Although it looks like the dome may have been mirrored in the middle, >which throws off some of the geodesic patterning, but at 167 hours >render-time, I don't really blame you. ;^) ) Glad you like it! It wasn't actually mirrored but the skewing was down to a cheap bit of coding I did. The utility I wrote to create the geodome data set started off with an octahedron and then recursively sub-divided each facet into smaller triangles. The problem with this is that the sides don't divide equally and you end up with this effect. What I *should* have done, and indeed now have, is to start with a dodecahedron which tessellates evenly. The new utility creates a whole load of other shapes too. When I get round to finishing it, I'll upload it somewhere and let you know where so the ray tracing fans amongst us can play with it. Cheers Andy This Spot Is Allowed whatever K says. Here, have some Andy Wardley chocolate, it's Terry's. No smug bait for Derek. M#0 abw@oasis.icl.co.uk Badgers are your friends. OK, so they don't frink but have you seen them forage? DAMN! I've run out of sp ========================================================================= Date: Mon, 1 Aug 1994 10:05:51 +0200 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: News-Reader XIAOMING UNSUBSCRIBE xiaoming xu ========================================================================= Date: Mon, 1 Aug 1994 08:29:52 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: Trimtab Sorry if this appears twice. More newsreader said 'posting failed'. I would appreciate it if someone could tell me if there has been a new issue of "Trimtab" since the Spring 1993 issue. It seems an awful long time since I got this one from the BFI and I wonder if I should chase them up about it. Regards Ross Keatinge icosa@iconz.co.nz Auckland New Zealand ========================================================================= Date: Mon, 1 Aug 1994 06:03:19 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: jpegs Sorry that I have to do this, but I lost my access to the Internet for a few weeks and would like to know where I can download the tensegrity jpeg from and the geodesic sphere. Thanks. Steve Mather ========================================================================= Date: Mon, 1 Aug 1994 06:45:56 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: IVM Someone mentioned a while back (when I couldn't post) that movement, according to theoretical physics, is in increments (not yet determined.) I had wondered if there was such a theory because energy/matter is alleged to move in very specific amounts as well. My problem with this, though in many ways it makes sense, is that then matter/energy is making tiny jumps through space/time. Am I wrong? Do I not understand it right? Steve Mather ========================================================================= Date: Mon, 1 Aug 1994 15:06:40 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: jpegs First of all (though I be late) I appreciated all of the jpegs. Just a question. What was the curve? Anything in particular? (no flame intended, I just want to know if it has any practical application.) Steve Mather ========================================================================= Date: Mon, 1 Aug 1994 21:59:36 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: Re: jpegs In-Reply-To: Message of Mon, 1 Aug 1994 15:06:40 GMT from On Mon, 1 Aug 1994 15:06:40 GMT said: >First of all (though I be late) I appreciated >all of the jpegs. >Just a question. What was the curve? Anything >in particular? (no flame intended, I just >want to know if it has any practical application.) The curve is not mine. I think it's Richard Hawkins'. It does demonstrate some of the relationships in the cube that are not necessarily obvious such as when you look at it topologically where each edge is a circle. I'm not sure of it's significance, but Bucky never doubted the significance of a pattern, so I won't :) I wish the image were larger and had different perspective, but the author has trouble with uuencoding (I'm working with him on it). > Steve Mather Christopher J. Fearnley cfearnl@pacs.pha.pa.us fearnlcj@duvm.ocs.drexel.edu fearnlcj@duvm.bitnet ========================================================================= Date: Tue, 2 Aug 1994 01:20:03 -0400 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Hawku Organization: America Online, Inc. (1-800-827-6364) Subject: Re: JPEGs Regarding the curVE file, the cube with circular rather than square faces is similar to the cuboctahedron (Vector Equilibrium) in that the vertices (or in this case tangents) are identical. The cuboctahedron (or VE without the radials) can be constructed from 4 hexagonal planes. Likewise the curVE model is constructed from 4 six-quadrant segments (blue,red,yellow,&green in the JPEG). The six quadrants each at 90 degrees to it's adjacents form a closed loop. Four of these loops make up the circumferentials of the model. The armatures (red and yellow in the JPEG) have their pivot point at the center of the system and are fixed to each other(grouped). The red armature revolves around each (six-quadrant) loop, switching where the loops intersect, through all 4 loops returning to the starting point ; while the yellow armature tracks the spherical triangles at the opposing ends of each of the 4 axes of rotation. Fuller's concept of 4D modeling alludes to the possibilities of 4 (or more) unique perpendiculars interacting in a system. The tetrahedron can have 4 unique perpendiculars (to it's faces), while the cube has only 3. This model is an attempt to demonstrate this concept. The yellow armature is in a precession relationship with the red. Its' movement is conical while the red revolves through 4 axes of rotation. I hope this helps to clarify. If not, perhaps I can upload an MPEG file somewhere (56 frames of animation). Richard Hawkins ========================================================================= Date: Tue, 2 Aug 1994 09:19:38 EST/EDT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: DAMICO@GELMAN.CIRC.GWU.EDU Subject: Re: In-line cable clamps Mitch clarifies his situation. > The poster suggested to look up references to 'Wire Rope' suppliers and > manufacturers in the Yellow Pages; this will obviously vary from area to > area - the Greater Rochester Yellow Pages has one entry under Wire Rope. > (Unfortunately, this local supplier has nothing in the scale of what I'm > interested in.) > I haven't had time to do any foot(phone)work lately, but the last round of > calls I made to a variety of possible suppliers turned up nothing. > -------------------------------------------------------------------------- > Mitch C. Amiano > amiano@delphi.com > I'll keep looking then. ========================================================================= Date: Tue, 2 Aug 1994 09:26:23 EST/EDT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: DAMICO@GELMAN.CIRC.GWU.EDU Subject: Re: LOOKING FOR SYNERGETICS II Pat writes: > > Well, here's a blatant plug, and a potential reference, since Chris F. > was asking about this via private email: My Synergy Ball is being produced by > Design Science Toys, of Tivoli, NY. They're the people who make the > Tensegritoys, Octabug, Hoberman Sphere, and a slew of other geodesic and > geometry based toys. They've got a nifty catalog which you can get by phoning > 1-800-227-2316. > > Just called and got my catalog sent to me. Thanks Pat. ========================================================================= Date: Tue, 2 Aug 1994 09:30:05 EST/EDT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: DAMICO@GELMAN.CIRC.GWU.EDU Subject: Re: LOOKING FOR SYNERGETICS II Pat > > > > Nice to be back. Thanks for keeping this going, people. It's great to > >see the interest out there! > Chris > We've come along way baby! I remember when the list was little more than you > (with growing amounts of help) getting everyone in the dorms at SUNY-Buffalo > interested in building a floating city :) Now, we have an ftp site and WWW > stuff out there! [PS: what is it with us SUNY students abandoning the state > that gave us so much?] I don't think that I ever mentioned that I attended SUNY at Buffalo for a year myself. ========================================================================= Date: Tue, 2 Aug 1994 09:35:06 EST/EDT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: DAMICO@GELMAN.CIRC.GWU.EDU Subject: Re: JPEGs [Clarification deleted] I hope this helps to clarify. If > not, perhaps I can upload an MPEG file somewhere (56 frames of animation). > Richard Hawkins > Clear concept or not I'd like to see the MPEG anyway. ========================================================================= Date: Thu, 4 Aug 1994 13:37:46 EDT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: BFI@AOL.COM Subject: Please send information on joining Please send information on joining Thank you Tony DeVarco Executive Director Buckminster Fuller Institute ========================================================================= Date: Fri, 5 Aug 1994 00:14:37 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: Re: Please send information on joining In-Reply-To: Message of Thu, 4 Aug 1994 13:37:46 EDT from On Thu, 4 Aug 1994 13:37:46 EDT said: >Please send information on joining > >Thank you > >Tony DeVarco >Executive Director >Buckminster Fuller Institute Did the move to Santa Barbara go well? I haven't received a Trimtab in ages - is one being planned soon? (Maybe my membership slipped - I guess I should check my checkbook :) It's good to have the institute involved - last month was one of the most exciting and info-filled months on the list ever (though we've been fairly active since last Sept/Oct and periodically active since 1989). I imagine this month will be equally active. BTW, I've done some work at getting the FAQ up-to-date through July '94 - but I need a few more weeks to tidy things up and fix a few bugs - for now everyone can get the FAQ from the list archives or anonymous ftp from switchboard.ftp.com in the /bucky directory. Do Enjoy! Christopher J. Fearnley UNIX SIG Leader at PACS cfearnl@pacs.pha.pa.us (Philadelphia Area Computer Society) fearnlcj@duvm.bitnet Design Science Revolutionary fearnlcj@duvm.ocs.drexel.edu Explorer in Universe 503 S 44th ST (215)349-9681 Philadelphia PA 1914-3907 ========================================================================= Date: Fri, 5 Aug 1994 19:13:34 -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: IVM >Someone mentioned a while back (when I couldn't >post) that movement, according to theoretical >physics, is in increments (not yet determined.) An interesting analog of entropy... I conjectured that, given that all energy appears to be quantized, and the energy of an object is a function of its mass and velocity, velocity should be quantized. Right ?-) > >I had wondered if there was such a theory because >energy/matter is alleged to move in very specific >amounts as well. > >My problem with this, though in many ways it makes >sense, is that then matter/energy is making tiny >jumps through space/time. I would also conjecture that for objects of matter, the net effects of a large number of discrete 'tiny jumps' would appear to be continuity of movement. For photons, questions of distance seem to make less sense. > >Am I wrong? Do I not understand it right? > Steve Mather > ------------------------------------------------------------------------ Mitch C. Amiano amiano@delphi.com ========================================================================= Date: Sat, 6 Aug 1994 10:56:20 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: The Butterfly Organization: Evolutionary Acceleration, Inc. Subject: Re: Please send information on joining BFI@AOL.COM writes: -Please send information on joining -Thank you -Tony DeVarco -Executive Director -Buckminster Fuller Institute Here's an old file I just dug up from my archives. I'm surprised it's still around, actually... (Gotta clean those old directories...) ------------------------------------------------------------------------------- To subscribe, send mail to LISTSERV@UBVM.BITNET and in the body of your letter put the line: SUB GEODESIC When you want to post, send mail to GEODESIC@UBVM.BITNET ******NOT***** to LISTSERV@UBVM.BITNET! LISTSERV@UBVM.BITNET is for subscriptions, administrivia, archive requests, etc. GEODESIC@UBVM.BITNET is the actual discussion group. Anything sent to GEODESIC will go to all members. (And you don't want to look like a jerk having everyone see your "SUB GEODESIC John Q. Public" command! ;^) ) This list is also linked to USENET in the group bit.listserv.geodesic You can subscribe to the list, [thereby helping us to have an accurate idea how many people are reading the group] and still read the messages through news, if you like. (That's what I do. I prefer not getting every post in my e-mail, but I want people to be able to find my address, if necessary.) If you'd like to be on the membership list, but not get mail, then after you subscribe, send mail to LISTSERV@UBVM.BITNET with the message SET GEODESIC NOMAIL This will remain in effect until you use SET GEODESIC MAIL to change it again. If you want to receive copies of everything you send to the list, use the command SET GEODESIC REPRO. If you DON'T want copies, use SET GEODESIC NOREPRO. (You may want to save this file to forward on to people who are interested, as it tells what the list is about, and how to subscribe.) Pat ______________________________Think For Yourself_______________________________ Patrick G. Salsbury 1800 Market Street #23, San Francisco, CA 94102 Voicemail: 415/703-7177 ------------------------------------------------------------------------------- I've seen the wiring under the board. :) -- Pat ______________________________Think For Yourself_______________________________ Patrick G. Salsbury 1800 Market Street #23, San Francisco, CA 94102 Voicemail: 415/703-7177 ------------------------------------------------------------------------------- I've seen the wiring under the board. :) ========================================================================= Date: Sat, 6 Aug 1994 19:38:44 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Nyrath Organization: TimeHeart Subject: Dymaxion car in "Addam's Family" Pardon me, but was that a Fuller style Dymaxion car that cousin It was driving in the movie "The Addam's Family"? Long torpedo shape, three wheels, one in the back, two in the front. Sure looked like one to me... ========================================================================= Date: Sat, 6 Aug 1994 14:33:18 -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: PI to 20 or 30 sig-figs ?? RE: Kirby Urner's July 8 posting: >I've come up with an algorithm for deriving pi that uses >no trig, just pythagoras. Using his algorithm, and after 33 iterations, I arrived at: 3.141592653589793239 [My program uses "long double" Think C variables on a Mac with no floating point chip.] I would like to check the validity of my program, but I don't have a definition of pi to that many places. So it would be helpful if someone could confirm this number for me. =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= Lee Wood | Lee_Wood@sfu.ca | INTJ spoken here. =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= ========================================================================= Date: Sat, 6 Aug 1994 14:38:00 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: Kirby Hey, whatever happened to Kirby? ========================================================================= Date: Sun, 7 Aug 1994 00:05:30 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: Re: Kirby In-Reply-To: Message of Sat, 6 Aug 1994 14:38:00 GMT from On Sat, 6 Aug 1994 14:38:00 GMT said: >Hey, whatever happened to Kirby? He posted that he was going to Africa with his family for a few weeks(?) He'll be back soon - judging from history he'll reply to all of the messages he has "missed." Chris Fearnley ========================================================================= Date: Sun, 7 Aug 1994 00:34:41 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: Re: PI to 20 or 30 sig-figs ?? In-Reply-To: Message of Sat, 6 Aug 1994 14:33:18 -0700 from On Sat, 6 Aug 1994 14:33:18 -0700 Lee Wood said: >RE: Kirby Urner's July 8 posting: >>I've come up with an algorithm for deriving pi that uses >>no trig, just pythagoras. > >Using his algorithm, and after 33 iterations, I arrived at: > > 3.141592653589793239 Very good! Here is my computer output to 28 decimal places: pi = 3.141592653589793238462643383. If you need more accuracy, I can increase the precision. > > >[My program uses "long double" Think C variables on a Mac >with no floating point chip.] > >I would like to check the validity of my program, but I don't >have a definition of pi to that many places. So it would be >helpful if someone could confirm this number for me. > >=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= >Lee Wood | >Lee_Wood@sfu.ca | INTJ spoken here. >=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= -- Christopher J. Fearnley UNIX SIG Leader at PACS cfearnl@pacs.pha.pa.us (Philadelphia Area Computer Society) fearnlcj@duvm.bitnet Design Science Revolutionary fearnlcj@duvm.ocs.drexel.edu Explorer in Universe 503 S 44th ST Linux Advocate Philadelphia PA 1914-3907 (215)349-9681 ========================================================================= Date: Sat, 6 Aug 1994 23:30:15 -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: PI to 20 or 30 sig-figs ?? RE: Chris Fearnley's post: > Very good! Here is my computer output to 28 decimal places: > pi = 3.141592653589793238462643383. If you need more accuracy, I can > increase the precision. I noticed that, while trying to "simplify" the equation, the program became unstable - resulting in SERIOUS roundoff errors So, considering how temperamental floating point numbers are, it's quite possible that my PI = 3.141592653589793239 and your pi = 3.141592653589793238462643383 are both way off the mark. I was actually hoping that someone had some absolutely authoritative source which *defines* PI to 100 sig-figs (or more!). =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= Lee Wood | Lee_Wood@sfu.ca | INTJ spoken here. =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= ========================================================================= Date: Sun, 7 Aug 1994 05:32:08 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: Re: PI to 20 or 30 sig-figs ?? In-Reply-To: Message of Sat, 6 Aug 1994 23:30:15 -0700 from On Sat, 6 Aug 1994 23:30:15 -0700 Lee Wood said: >RE: Chris Fearnley's post: > >> Very good! Here is my computer output to 28 decimal places: >> pi = 3.141592653589793238462643383. If you need more accuracy, I can >> increase the precision. > >I noticed that, while trying to "simplify" the equation, >the program became unstable - resulting in SERIOUS roundoff errors > >So, considering how temperamental floating point numbers are, >it's quite possible that my > >PI = 3.141592653589793239 > >and your > >pi = 3.141592653589793238462643383 > >are both way off the mark. > Very unlikely - I used the PARI/gp unlimited precision calculator. I think it keeps 100 sig-figs (it spits it out awfully fast). I think it's a pretty authoritative result. So you did something right! I was not using an algorithm, but a mathematical package. > >I was actually hoping that someone had some absolutely >authoritative source which *defines* PI to 100 sig-figs >(or more!). >=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= >Lee Wood | >Lee_Wood@sfu.ca | INTJ spoken here. >=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= Christopher J. Fearnley UNIX SIG Leader at PACS cfearnl@pacs.pha.pa.us (Philadelphia Area Computer Society) fearnlcj@duvm.bitnet Design Science Revolutionary fearnlcj@duvm.ocs.drexel.edu Explorer in Universe 503 S 44th ST Linux Advocate Philadelphia PA 1914-3907 (215)349-9681 ========================================================================= Date: Sun, 7 Aug 1994 16:39:58 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: PI to 20 or 30 sig-figs ?? In Article <199408062133.OAA10992@whistler.sfu.ca> Lee Wood writes: >RE: Kirby Urner's July 8 posting: >>I've come up with an algorithm for deriving pi that uses >>no trig, just pythagoras. > >Using his algorithm, and after 33 iterations, I arrived at: > 3.141592653589793239 here's what I found, below your own: 3.14159265358979323846264338327950... >[My program uses "long double" Think C variables on a Mac >with no floating point chip.] > >I would like to check the validity of my program, but I don't >have a definition of pi to that many places. So it would be >helpful if someone could confirm this number for me. I don't know how many places that is. COUNT THEM YOURSELF! =) My eyes hurt now. Steve Mather ========================================================================= Date: Mon, 8 Aug 1994 08:52:47 -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: PI to 20 or 30 sig-figs ?? The reason for my apparent obsession with the number of significant digits in my results is as following: In the first iteration, my hypotenuse is simply the square root of 2. And it is used to derive the new hypotenuse. newH = sqrt( pow(h/2,2) + pow(1-sqrt(1-pow(h/2,2)),2) ); i.e. h= 1.4142135623730950490 newH= 0.7653668647301795434 Notice that these results contain about 20 sig-figs. However, by the time I've done 32 iterations, my new hypotenuse has shrunk to only 10 sig-figs. newH=0.0000000007314590396 But my value for PI, based on that hypotenuse, shows 19 sig-figs. PI= 3.141592653589793239 It's been about 20 years since I took Physics-101, but I'm fairly certain that one of the points they tried to drive home was that one cannot generate sig-figs out of thin air. i.e. If one of the numbers in my calculation has only 10 sig-figs, then the end product of the calculation is only significant to 10 digits. And I should simply discard any digits beyond that. So, I should only be permitted to say: PI= 3.141592653 The fact that there is such a close correspondence between my longer value and the PI generated by Chris Fearnley's canned math routine, frankly, has me puzzled. Theoretically, I should not be that close to the correct value. canned pi= 3.141592653589793238462643383 My PI= 3.141592653589793239 Chris, I would be interested to see if any of those low-end digits change as you double or triple your precision. Steve Mather reports an astounding: 3.14159265358979323846264338327950... i.e. Steve's Pi= 3.14159265358979323846264338327950... Chris' pi= 3.141592653589793238462643383 My PI= 3.141592653589793239 Steve, did you use a canned routine or write a program? If the latter, I'd be *very* interested in seeing your source code. =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= Lee Wood | Lee_Wood@sfu.ca | INTJ spoken here. =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= ========================================================================= Date: Mon, 8 Aug 1994 13:26:28 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: Re: PI to 20 or 30 sig-figs ?? In-Reply-To: Message of Mon, 8 Aug 1994 08:52:47 -0700 from On Mon, 8 Aug 1994 08:52:47 -0700 Lee Wood said: [Significant digits stuff deleted] > >The fact that there is such a close correspondence between my >longer value and the PI generated by Chris Fearnley's canned >math routine, frankly, has me puzzled. Theoretically, I should >not be that close to the correct value. I'm not following all this, but maybe your program is better than you thought? > >canned pi= 3.141592653589793238462643383 >My PI= 3.141592653589793239 > > >Chris, I would be interested to see if any of those low-end >digits change as you double or triple your precision. Here are 100 significant digits: pi = 3.1415926535897932384626433832795028841971693993 75105820974944592307816406286208998628034825342117068 > >i.e. >Steve's Pi= 3.14159265358979323846264338327950... >Chris' pi= 3.141592653589793238462643383 >My PI= 3.141592653589793239 > >Steve, did you use a canned routine or write a program? >If the latter, I'd be *very* interested in seeing your source code. Apperently the pari calulator has some algorithm for calculating higher sig digits here is the initial definition (from the source): #ifndef PI const double PI = 3.141592653589; /* pi */ #endif This function is probably where it happens: void constpi(long prec) I think I got PARI/gp (for DOS, Unix and I think Amiga and Mac too, but I'm not sure) from megrez.ceremab.u-bordeaux.fr (147.210.16.17) by ftp. If you like I could probably find the actual function (I bet they use Taylor polynomials) that calculates PI in pari/gp. But the program was written by number theorists for speed and accuracy not synergetics :) >=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= >Lee Wood | >Lee_Wood@sfu.ca | INTJ spoken here. >=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= ========================================================================= Date: Mon, 8 Aug 1994 13:35:45 EST/EDT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: DAMICO@GELMAN.CIRC.GWU.EDU Subject: Re: Dymaxion car in "Addam's Family" > Subject: Dymaxion car in "Addam's Family" > To: Multiple recipients of list GEODESIC > > > Pardon me, but was that a Fuller style Dymaxion car that > cousin It was driving in the movie "The Addam's Family"? > Long torpedo shape, three wheels, one in the back, two in the > front. > Sure looked like one to me... > Which one, Addams 2?"Just call me Trimtab" RBF _______ / \ BDAMICO@GWUVM.GWU.EDU ___________/__________\____________ \ Trimtab: A tiny gear / |\ which moves the rudder / |__\ that turns great ships / --------------------- ========================================================================= Date: Mon, 8 Aug 1994 14:26:35 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: PI to 20 or 30 sig-figs ?? In Article <199408081552.IAA00398@whistler.sfu.ca> Lee Wood writes: >The reason for my apparent obsession with the number of >significant digits in my results is as following: > >In the first iteration, my hypotenuse is simply the square >root of 2. And it is used to derive the new hypotenuse. > >newH = sqrt( pow(h/2,2) + pow(1-sqrt(1-pow(h/2,2)),2) ); I don't think I understand how one is used to determine the next. Could you explain? (I hate ASCII characters =) >Steve Mather reports an astounding: >3.14159265358979323846264338327950... The University of Toledo's Gopher server has it to 1 million signifigant figures. Check w/them. See my other post (note-- not U of Mich.) Steve Mather ========================================================================= Date: Mon, 8 Aug 1994 13:55:46 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: PI to 20 or 30 sig-figs ?? In Article <199408081552.IAA00398@whistler.sfu.ca> Lee Wood writes: >The reason for my apparent obsession with the number of >significant digits in my results is as following: > >In the first iteration, my hypotenuse is simply the square >root of 2. And it is used to derive the new hypotenuse. > >newH = sqrt( pow(h/2,2) + pow(1-sqrt(1-pow(h/2,2)),2) ); > >i.e. >h= 1.4142135623730950490 >newH= 0.7653668647301795434 > >Notice that these results contain about 20 sig-figs. > > > >However, by the time I've done 32 iterations, my new >hypotenuse has shrunk to only 10 sig-figs. > >newH=0.0000000007314590396 > >But my value for PI, based on that hypotenuse, shows >19 sig-figs. > >PI= 3.141592653589793239 > > >It's been about 20 years since I took Physics-101, but I'm >fairly certain that one of the points they tried to drive >home was that one cannot generate sig-figs out of thin air. > >i.e. If one of the numbers in my calculation has only >10 sig-figs, then the end product of the calculation is >only significant to 10 digits. And I should simply discard >any digits beyond that. > >So, I should only be permitted to say: > >PI= 3.141592653 > > > >The fact that there is such a close correspondence between my >longer value and the PI generated by Chris Fearnley's canned >math routine, frankly, has me puzzled. Theoretically, I should >not be that close to the correct value. > >canned pi= 3.141592653589793238462643383 >My PI= 3.141592653589793239 > > >Chris, I would be interested to see if any of those low-end >digits change as you double or triple your precision. > > > >Steve Mather reports an astounding: >3.14159265358979323846264338327950... > >i.e. >Steve's Pi= 3.14159265358979323846264338327950... >Chris' pi= 3.141592653589793238462643383 >My PI= 3.141592653589793239 > >Steve, did you use a canned routine or write a program? >If the latter, I'd be *very* interested in seeing your source code. I found that number in gopher (sorry, didn't mean to imply I programmed it, I can barely program =) I think it was at the U of Michigan in Ann Arbor. I'll have to check it out. They've got it to a million places, and that's what I wrote down from it a long time ago. Gimme a couple days and I'll track the source down for you.... Steve Mather ========================================================================= Date: Mon, 8 Aug 1994 22:23:04 -0400 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: SYoke Organization: America Online, Inc. (1-800-827-6364) Subject: Re: Dymaxion car in "Addam's Family" In article <320os4$p51@clarknet.clark.net>, nyrath@clark.net (Nyrath) writes: Pardon me, but was that a Fuller style Dymaxion car that cousin It was driving in the movie "The Addam's Family"? Long torpedo shape, three wheels, one in the back, two in the front. Sure looked like one to me... No. That car was a Messerschmidt Tiger, a bubble car built by the same co. that built Nazi planes in WWII. The Germans built cars with three wheels because they went in a lower automobile tax bracket after WWII, and not many Germans after WWII could even afford these small cars. ========================================================================= Date: Mon, 8 Aug 1994 22:29:33 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Bob Cook Subject: Help design the Tucson Solar Village Tucson Solar Village GEODESIC Delphi Questionaire For all of you in GEODESIC interested in the challenges of developing an actual "eco-village", here is your once in a decade opportunity to help us think through the final pre-construction phase of the Tucson Solar Village Program. The Tucson Solar Village is an ongoing program sponsored by the Tucson- Pima County Metropolitan Energy Commission and the City of Tucson to demonstrate that communities can be designed, built, marketed and lived in, in a more sustainable manner by: 1- Greatly increasing the efficiency of how energy, water and other resources are used; 2- Significantly reducing our impact on the natural environment; 3- Providing a lifestyle rich in variety, opportunities, amenities and sense of community; 4- Reducing dependence upon public services for transportation, security and other infrastructure. This starts a 10-week intensive planning effort with the objective of developing a Comprehensive Implementation Strategy for approval by City and State governments with assurance of cooperation by all parties involved. This process has four parts: 1- A Delphi process with 3 successive questionnaires to identify critical implementation issues and strategies; 2- Two workshops to help analyze the results of the Delphi process and integrate them into a comprehensive plan; 3- Critical review and comment which will include local, state and national experts; and 4- Public Forum for final review and information-sharing. The Metropolitan Energy Commission is seeking your thoughtful assistance to help achieve its dual goals of successful development of Civano and transfer of those concepts to the larger community. Please take a few moments, focus on the need to bring the vision of the Solar Village into reality from a development perspective, and answer the attached questionnaire. This first questionnaire is intended to be very general and somewhat open-ended. The succeeding two questionnaires will incorporate responses from the previous ones and will become more detailed and specific. Please E-mail or fax your responses in time to be received by Tuesday, August 16, 1994 to: Robert Cook, Acting Chair, Solar Village Steering Committee, Tucson-Pima County Metropolitan Energy Commission E-mail: BCook@Pimacc.Pima.Edu or FAX (602) 748-4754 For any other information, I can be reached by voice mail at: (602) 748- 4743 or s-mail: P.O. Box 41144 Tucson AZ 85717 Your responses, together with those of other participants, will help form the basis of a second questionnaire which will be sent to you about August 20, 1994. Thank you very much for your participation. PROJECT STATUS >From its inception, The Solar Village has been a cooperative effort between the public and private sectors on many levels. There are several phases to the project. PHASE 1 ended in the Spring of 1992 with the preparation of a Master Development Plan for Civano, an 820 acre mixed use community for 5600 people within the City of Tucson. This development plan, together with appropriate zoning, was approved unanimously by the Mayor and Council and subsequently formally adopted by the Arizona State Land Department, which owns the property as part of the State Urban Lands Trust. The adopted documents include Covenants, Conditions and Restrictions (CC&Rs) which guide the future design and decision-making regarding physical development and future governance of the land. General performance targets for resource efficiency and amenities include areas such as energy demand, water consumption, solid waste flows, affordability, landscape/land use, job-creation/employment oppportunities, and sustainable transportation in the village. This plan and public involvement process was awarded the "Best Project of 1992" by the Arizona Planning Association. PHASE 2 is soon ending with the preparation of a series of performance standards which will guide the design and development of all buildings within Civano. PHASE 3 is beginning now with detailed implementation planning to assure Civano's successful development and ways to expand its concepts and vision to the broader community. Because the Solar Village concept departs from conventional approaches to development, there are many issues which still need to be resolved in order to achieve its potential. Currently, the Arizona State Land Department is preparing a final appraisal for Civano based upon the land value, the adopted Master Development Plan, the current zoning, and the completed Performance Standards. This appraisal is currently scheduled to be finalized by December, 1994. Within six months after this date, a public auction can be held if the State Land Department chooses. The Metropolitan Energy Commission is particularly concerned with fostering -Continued building of consensus and cooperation between the public and private sectors at all levels, -Active participation by forward-thinking, energetic, enthusiastic and pro-active community leaders, and -Recruitment and selection of developers and builders who understand and are committed to the same vision. THE TUCSON SOLAR VILLAGE PROGRAM COMPREHENSIVE IMPLEMENTATION STRATEGY DELPHI QUESTIONNAIRE: CYCLE 1, GENERAL QUESTIONS This is the first cycle of a 3-cycle Delphi process to identify key issues and strategies preparatory to planning Phase 3 of the Solar Village Program, leading to construction. We are interested in your creativity and judgement and are looking for good ideas. All responses will be confidential and none will be associated with a name or organization. Please respond to be received by Tuesday, August 16. Thank you very much. 1. The Civano project of the Tucson Solar Village proposes to bring together the best and most recent developments in many fields. What distinquishing features or innovations to make this special and attractive would you most like to see in such a development? 2. The challenge of implementing this innovative land development project requires a well thought-out approach. What set of activities are most needed to assure Civano's success and accomplish such goals as you identified in question 1? (To answer this you might consider, for example, technology, marketing, financing, and other feasibility issues) 3. The Solar Village Program also seeks to bring the benefits of Civano to all of Tucson. What are the most important aspects of Civano that you think could and should be implemented in the community at large? 4. Considering your responses to both questions 2 and 3, how can we bring together the best people with the right resources to get the job done? 5. What questions should be included in the next two cycles of the questionnaire? ========================================================================= Date: Tue, 9 Aug 1994 09:51:23 -0400 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "James E. Hoburg" Subject: Re: PI to 20 or 30 sig-figs ?? In-Reply-To: <199408090325.XAA11517@dialup.oar.net> Steve Mather writes: > I found that number in gopher (sorry, didn't mean to > imply I programmed it, I can barely program =) > I think it was at the U of Michigan in Ann Arbor. > I'll have to check it out. They've got it to > a million places, and that's what I wrote down from it > a long time ago. > > Gimme a couple days and I'll track the source down for > you.... Excerpted from the newsgroup sci.math FAQ => [...] 4Q: Where I can get pi up to a few hundred thousand digits of pi? Does anyone have an algorithm to compute pi to those zillion decimal places? A: MAPLE or MATHEMATICA can give you 10,000 digits of Pi in a blink, and they can compute another 20,000-1,000,000 overnight (range depends on hardware platform). It is possible to retrieve 1.25+ million digits of pi via anonymous ftp from the site wuarchive.wustl.edu, in the files pi.doc.Z and pi.dat.Z which reside in subdirectory doc/misc/pi. New York's Chudnovsky brothers have computed 2 billion digits of pi on a homebrew computer. How is pi calculated to many decimals ? There are essentially 3 different methods. 1) One of the oldest is to use the power series expansion of atan(x) atan(x)=x-x^3/3+x^5/5-... together with formulas like pi=16*atan(1/5)-4*atan(1/239). This gives about 1.4 decimals per term. 2) A second is to use formulas coming from Arithmetic-Geometric mean computations. A beautiful compendium of such formulas is given in the book of Borwein and Borwein: Pi and the AGM, Canadian Math. Soc. Series, John Wiley and Sons, New York, 1987. They have the advantage of converging quadratically, i.e. you double the number of decimals per iteration. For instance, to obtain 1 000 000 decimals, around 20 iterations are sufficient. The disadvantage is that you need FFT type multiplication to get a reasonable speed, and this is not so easy to program. 3) A third one comes from the theory of complex multiplication of elliptic curves, and was discovered by S. Ramanujan. This gives a number of beautiful formulas, but the most useful was missed by Ramanujan and discovered by the Chudnovsky's. It is the following (slightly modified for ease of programming): Set k1=545140134;k2=13591409;k3=640320;k4=100100025;k5=327843840;k6=53360; Then in AmsTeX notation $\pi=\frac{k6\sqrt(k3)}{S}$, where $$S=\sum_{n=0}^\infty (-1)^n\frac{(6n)!(k2+nk1)}{n!^3(3n)!(8k4k5)^n}$$ The great advantages of this formula are that 1) It converges linearly, but very fast (more than 14 decimal digits per term). 2) The way it is written, all operations to compute S can be programmed very simply since it only involves multiplication/division by single precision numbers. This is why the constant 8k4k5 appearing in the denominator has been written this way instead of 262537412640768000. This is how the Chudnovsky's have computed several billion decimals. Question: how can I get a C program which computes pi? Answer: if you are too lazy to use the hints above, you can use the following 160 character C program (who is the author of this?) which computes pi to 800 decimal digits. If you want more, it is easy to modify, but you have to understand how it works first. int a=10000,b,c=2800,d,e,f[2801],g;main(){for(;b-c;)f[b++]=a/5; for(;d=0,g=c*2;c-=14,printf("%.4d",e+d/a),e=d%a)for(b=c;d+=f[b]*a, f[b]=d%--g,d/=g--,--b;d*=b);} References : (This is a short version for a more comprehensive list contact Juhana Kouhia at jk87377@cc.tut.fi) J. M. Borwein, P. B. Borwein, and D. H. Bailey, "Ramanujan, Modular Equations, and Approximations to Pi", American Mathematical Monthly, vol. 96, no. 3 (March 1989), p. 201 - 220. P. Beckman A history of pi Golem Press, CO, 1971 (fourth edition 1977) J.M. Borwein and P.B. Borwein The arithmetic-geometric mean and fast computation of elementary functions SIAM Review, Vol. 26, 1984, pp. 351-366 J.M. Borwein and P.B. Borwein More quadratically converging algorithms for pi Mathematics of Computation, Vol. 46, 1986, pp. 247-253 J.M. Borwein and P.B. Borwein Pi and the AGM - a study in analytic number theory and computational complexity Wiley, New York, 1987 Shlomo Breuer and Gideon Zwas Mathematical-educational aspects of the computation of pi Int. J. Math. Educ. Sci. Technol., Vol. 15, No. 2, 1984, pp. 231-244 David Chudnovsky and Gregory Chudnovsky The computation of classical constants, Columbia University, Proc. Natl. Acad. Sci. USA, Vol. 86, 1989. Y. Kanada and Y. Tamura Calculation of pi to 10,013,395 decimal places based on the Gauss-Legendre algorithm and Gauss arctangent relation Computer Centre, University of Tokyo, 1983 Morris Newman and Daniel Shanks On a sequence arising in series for pi Mathematics of computation, Vol. 42, No. 165, Jan 1984, pp. 199-217 E. Salamin Computation of pi using arithmetic-geometric mean Mathematics of Computation, Vol. 30, 1976, pp. 565-570 D. Shanks and J.W. Wrench, Jr. Calculation of pi to 100,000 decimals Mathematics of Computation, Vol. 16, 1962, pp. 76-99 Daniel Shanks Dihedral quartic approximations and series for pi J. Number Theory, Vol. 14, 1982, pp.397-423 David Singmaster The legal values of pi The Mathematical Intelligencer, Vol. 7, No. 2, 1985 Stan Wagon Is pi normal? The Mathematical Intelligencer, Vol. 7, No. 3, 1985 J.W. Wrench, Jr. The evolution of extended decimal approximations to pi The Mathematics Teacher, Vol. 53, 1960, pp. 644-650 [...] ========================================================================= Date: Tue, 9 Aug 1994 09:39:50 -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: PI to 20 or 30 sig-figs ?? Steve Mather wrote: LW>>In the first iteration, my hypotenuse is simply the square LW>>root of 2. And it is used to derive the new hypotenuse. LW>> LW>>newH = sqrt( pow(h/2,2) + pow(1-sqrt(1-pow(h/2,2)),2) ); SM> I don't think I understand how one is used to determine SM> the next. Could you explain? (I hate ASCII characters =) After trying several times to draw a circle, incsribed square, etc. with ASCII characters, I gave up and drew it on a "CAD" program. (MacDraw II for you Mac fans) If you like, I'd be glad to FAX you the three page output. =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= Lee Wood | Lee_Wood@sfu.ca | INTJ spoken here. =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= ========================================================================= Date: Tue, 9 Aug 1994 16:59:15 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "David Q. Spitzley" Organization: Illuminati Online (on pentagon) Subject: World Game Does anyone out there have any details on how to get a copy of the rules for the World Game, or any comments from experience on running it "off-campus", i.e. outside it's normal residence? ========================================================================= Date: Tue, 9 Aug 1994 13:14:53 EST/EDT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: DAMICO@GELMAN.CIRC.GWU.EDU Subject: Re: World Game "David Q. Spitzley" writes > Does anyone out there have any details on how to get a copy of the rules > for the World Game, or any comments from experience on running it > "off-campus", i.e. outside it's normal residence? > I have to check for the address of the World Game institute in Penn. (unless someone beats me to it). The institute was at GWU two years ago to run a Game. About 30 people participated and it was an education as well as fun. I will locate my old post that described the experience. Have you seen the Hypercard stack from the World Game Institute? I've seen it offered from BFI but haven't gotten a copy myself."Just call me Tri mtab" RBF _______ / \ BDAMICO@GWUVM.GWU.EDU ___________/__________\____________ \ Trimtab: A tiny gear / |\ which moves the rudder / |__\ that turns great ships / --------------------- ========================================================================= Date: Tue, 9 Aug 1994 14:10:06 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: Kirby In Article Chris Fearnley writes: >On Sat, 6 Aug 1994 14:38:00 GMT said: >>Hey, whatever happened to Kirby? >He posted that he was going to Africa with his family for a few weeks(?) >He'll be back soon - judging from history he'll reply to all of the >messages he has "missed." On that note, where would I find the archives? Steve Mather ========================================================================= Date: Tue, 9 Aug 1994 23:56:56 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: Re: World Game In-Reply-To: Message of Tue, 9 Aug 1994 16:59:15 GMT from On Tue, 9 Aug 1994 16:59:15 GMT David Q. Spitzley said: >Does anyone out there have any details on how to get a copy of the rules >for the World Game, or any comments from experience on running it >"off-campus", i.e. outside it's normal residence? We all play the world game every day :) But there is an organization devoted to Bucky concept of the World Game. The World Game Institute 3215 Race Street Philadelphia, PA 19104-2597 Phone: (215)387-0220 Fax: (215)387-3009 The basic rule is to make the world work for 100% of humanity in the shortest period of time without ecological offense nor the disadvantage of anyone (rough paraphrase of Bucky there) -- Christopher J. Fearnley | UNIX SIG Leader at PACS cfearnl@pacs.pha.pa.us | (Philadelphia Area Computer Society) fearnlcj@duvm.bitnet | Design Science Revolutionary fearnlcj@duvm.ocs.drexel.edu | Explorer in Universe 503 S 44th ST | Linux Advocate Philadelphia PA 1914-3907 | (215)349-9681 ========================================================================= Date: Wed, 10 Aug 1994 21:35:04 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 Chris Fearnley writes: >On Tue, 9 Aug 1994 16:59:15 GMT David Q. Spitzley said: >>Does anyone out there have any details on how to get a copy of the rules >>for the World Game, or any comments from experience on running it >>"off-campus", i.e. outside it's normal residence? >We all play the world game every day :) But there is an organization >devoted to Bucky concept of the World Game. >The World Game Institute >3215 Race Street >Philadelphia, PA 19104-2597 >Phone: (215)387-0220 Fax: (215)387-3009 >The basic rule is to make the world work for 100% of humanity in the shortest >period of time without ecological offense nor the disadvantage of anyone >(rough paraphrase of Bucky there) World Game Institute produces a (typically 3-4 hour) workshop which serves as an introduction to the concepts of World Game, as described by Bucky. In the last 20 years, 90,000 people have participated in workshops held for universities, corporations, high schools, churches, government agencies, and others all over the world. We also do World Game Workshops with a focus (diversity, environment). We're (finally) putting together an excerpt from an upcoming brochure that I can send via e-mail. Also, I have brief descriptions of other products and programs we provide (atlas and database software, playground maps, etc.) If you're interested in that information, our e-mail address is xtm00002@duvm.ocs.drexel.edu. For further information, please call or write (see above). As for comments and experiences of past participants at the workshops, I look forward to seeing them posted here. I've worked for WGI for 11 years and have been repeatedly amazed by the positive responses of participants and hosts. We currently have posted on our bulletin board a letter from a woman whose father-in-law expressed a desire before he died that his grandchildren participate in a grade school version of the workshop he had observed. Dane Winberg World Game Institute ========================================================================= Date: Wed, 10 Aug 1994 19:53:06 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "by way of woodh@sfu.ca Lee Wood" Subject: Bad Address for a DCA User The Internet address you are using for Darren Cromer at DCA is no longer valid, Please discontinue its use. Thanks, Robert C. Covington Director, MIS Operations Digital Communications Associates Voice: (404)442-4887 FAX: (404)442-4361 X.400: c=us; ad=attmail; pr=dca; su=covington; gi=robert Internet: itrcc@dcatla.com ========================================================================= Date: Thu, 11 Aug 1994 07:37:00 -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: Bad Address for a DCA User I've been receiving "bounce" warnings each time I post something to this list. And eventually I got the following. This looks like a job for the list owner. ___________________________________________________________________ > The Internet address you are using for Darren Cromer at DCA is >no longer valid, Please discontinue its use. > >Thanks, > >Robert C. Covington >Director, MIS Operations >Digital Communications Associates >Voice: (404)442-4887 >FAX: (404)442-4361 >X.400: c=us; ad=attmail; pr=dca; su=covington; gi=robert >Internet: itrcc@dcatla.com ========================================================================= Date: Thu, 11 Aug 1994 23:53:58 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: Re: Bad Address for a DCA User In-Reply-To: Message of Thu, 11 Aug 1994 07:37:00 -0700 from On Thu, 11 Aug 1994 07:37:00 -0700 Lee Wood said: >I've been receiving "bounce" warnings each time I post something >to this list. And eventually I got the following. > Yes, the problem should be solved soon. I e-mailed the administrator of the bad account telling him how to fix it. And our list owner might beat him to the punch :) > ========================================================================= Date: Fri, 12 Aug 1994 20:14:21 -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: PI to 20 or 30 sig-figs ?? Ah, the thread awakens... It reminds me of something I read recently: "... Formalism was quite secondary to the to the informal reasoning that is carried out when mathematicians have a first idea about the sort of theorem that they would like to prove; they attempt to do this, and discover that it can't be done because there are unusual counterexamples to their potential theorem. Their response is to first revise and refine their goal and then to try to prove a new theorem. Lakatos showed how some geometrical problems had evolved in this way through a chain of reformulations, counterexamples, and partial proofs until something related to - but quite distinct from - the original proposal was stated and proved. ..." - John D. Barrow, in "PI in the Sky," referencing Imre Lakatos' "Proofs and Refutations" Incidentally, my original effort was aimed at developing a rational approximation of pi as a function of the frequency of a regular polygon, without trig. Leaving out the later restriction, I came up with: /----------------------------------------- pi' = n * \/ (R - R*cos(360/n) )^2 + ( R*sin(360/n) )^2 ---------------------------------------------------- 2*R Where n = frequency of subdivision and R = radius of circumscribing circle. --------------------------------------------------------------------------- Mitch C. Amiano amiano@delphi.com ========================================================================= Date: Sat, 13 Aug 1994 02:24:21 -0400 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Shannon A Snider Subject: AIP Fullerene News For those of you on GEODESIC who may be interested in the ongoing research research into Fullerenes (or Buckyballs). A morsel of information distributed by the American Institute of Physics... - Shannon A. Snider Forwarded message: > PHYSICS NEWS UPDATE > A digest of physics news items by Phillip F. Schewe, American > Institute of Physics > Number 189 August 9, 1994 physnews@aip.org > > THAT METAL ATOMS CAN SIT INSIDE BUCKYBALLS has now > been proved by an IBM Almaden-Caltech-Virginia Polytechnic > collaboration. Using transmission electron microscopy, the physicists > showed that the lattice spacing for a pure crystals of C-84 molecules > was the same (11.2 angstroms) as that for a crystal of Sc2@C84 > molecules, the first such pure metallofullerene crystal to be prepared. > They assert that the Sc2@C84 molecules are truly endohedral; that is, > the metal atoms reside within and not alongside the fullerenes. (R. > Beyers et al., Nature, 21 July.) ========================================================================= Date: Mon, 15 Aug 1994 03:09:07 -0400 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: CPofLA Organization: America Online, Inc. (1-800-827-6364) Subject: Bucky Ball Kit For a flyer featuring a very cool (well that's what we say) bucky ball kit, contact mondo@mondo.com or call 1 415 455 9330. Chris Paine ========================================================================= Date: Wed, 17 Aug 1994 09:33:58 PDT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: AMMSSC@TEVM2.NSC.COM Subject: NO SUBJECT X-To: geodesic%ubvm.bitnet@mitvma.mit.edu FROM: Mike Slama SUBJECT: subscribe geodesic Mike Slama ========================================================================= Date: Fri, 19 Aug 1994 01:44:34 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: Q: Uniquely identifying dome segments For a project we are working on we need to uniquely identify each of the faces of a subdivided spherical icosahedron (more specifically, we need some addressing system for dealing with the faces on a computer). A colleague came-up with an interesting line of investigation: does anyone know how the individual faces of a geodesic dome are identified/ marked so that they can be correctly assembled? Thanks, Kevin ========================================================================= Date: Fri, 19 Aug 1994 14:49:53 EST Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "j.marang-acacia-dsn-student-91093738" Subject: Fog Gun anyone? Hi! I just popped onto this list in the hope that someone here could give me some information on an invention of Buckminster's known as a 'Fog Gun'. A lecturer ofmine told me about this invention and he used that name, so I hope it's right. It's been impossible so far to find any information on the invention, because all of the books I've found so far only deal with his major inventions, like thegeodesic domes. Buckminster (so my lecturer tells me) came up with the idea after observing some fishermen coming back after fishing in a fog. Their hands, which should have been oily and dirty, were completely clean. He hypothesised that the combination of fog and high wind had an efficient cleaning effect. He invented a device that forced water through a nozzle to create a fine mist, and a heating device was located at the junction between the hose and nozzle. This is all I know, and I don't know how acurate it is. Can anyone supply me with more information? Thanks, Jennifer jlmarang@acacia.itd.uts.edu.au ========================================================================= Date: Fri, 19 Aug 1994 15:25:07 EST Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "j.marang-acacia-dsn-student-91093738" Subject: Fog Gun anyone? Forwarded message: >From jlmarang Fri Aug 19 14:50:06 1994 From: jlmarang (j.marang-acacia-dsn-student-91093738) Message-Id: <9408190449.AA10052@acacia.itd.uts.EDU.AU> Subject: Fog Gun anyone? To: geodesic@ubvm.bitnet Date: Fri, 19 Aug 94 14:49:53 EST Cc: jlmarang X-Mailer: ELM [version 2.4dev PL17] Hi! I just popped onto this list in the hope that someone here could give me some information on an invention of Buckminster's known as a 'Fog Gun'. A lecturer ofmine told me about this invention and he used that name, so I hope it's right. It's been impossible so far to find any information on the invention, because all of the books I've found so far only deal with his major inventions, like thegeodesic domes. Buckminster (so my lecturer tells me) came up with the idea after observing some fishermen coming back after fishing in a fog. Their hands, which should have been oily and dirty, were completely clean. He hypothesised that the combination of fog and high wind had an efficient cleaning effect. He invented a device that forced water through a nozzle to create a fine mist, and a heating device was located at the junction between the hose and nozzle. This is all I know, and I don't know how acurate it is. Can anyone supply me with more information? Thanks, Jennifer jlmarang@acacia.itd.uts.edu.au ========================================================================= Date: Fri, 19 Aug 1994 15:52:40 EST Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "j.marang-acacia-dsn-student-91093738" Subject: Fog Gun anyone? Forwarded message: >From jlmarang Fri Aug 19 14:50:06 1994 From: jlmarang (j.marang-acacia-dsn-student-91093738) Message-Id: <9408190449.AA10052@acacia.itd.uts.EDU.AU> Subject: Fog Gun anyone? To: geodesic@ubvm.bitnet Date: Fri, 19 Aug 94 14:49:53 EST Cc: jlmarang X-Mailer: ELM [version 2.4dev PL17] Hi! I just popped onto this list in the hope that someone here could give me some information on an invention of Buckminster's known as a 'Fog Gun'. A lecturer of mine told me about this invention and he used that name, so I hope it's right. It's been impossible so far to find any information on the invention, because all of the books I've found so far only deal with his major inventions, like the geodesic domes. Buckminster (so my lecturer tells me) came up with the idea after observing some fishermen coming back after fishing in a fog. Their hands, which should have been oily and dirty, were completely clean. He hypothesised that the combination of fog and high wind had an efficient cleaning effect. He invented a device that forced water through a nozzle to create a fine mist, and a heating device was located at the junction between the hose and nozzle. This is all I know, and I don't know how acurate it is. Can anyone supply me with more information? Thanks, Jennifer jlmarang@acacia.itd.uts.edu.au ========================================================================= Date: Fri, 19 Aug 1994 02:10:42 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: Re: Fog Gun anyone? In-Reply-To: Message of Fri, 19 Aug 1994 14:49:53 EST from On Fri, 19 Aug 1994 14:49:53 EST j.marang-acacia-dsn-student-91093738 said: >Hi! > >I just popped onto this list in the hope that someone here could give me some > information on an invention of Buckminster's known as a 'Fog Gun'. A lecturer > ofmine told me about this invention and he used that name, so I hope it's > right. Here is what I've compiled on the fog gun from the FAQ: Pat Salsbury originally posted the following: The ``fog gun'' was an invention Bucky developed as a water saving alternative to the wastefulness of showers. While Bucky was in the navy, he noted that, while standing on the deck of a ship, in the spray and mist of the sea, nothing seems to stay on your skin for very long. Not even grease. He reasoned that it must have something to do with the abrasive action of the tiny water droplets, so he developed a device that atomized the water (like a perfume bottle with the little bulb that you squeeze to get perfume mist) and ejected it at high speed. He dubbed this the ``fog gun'' and found that it worked very well for cleaning a person off without soap (I'm not sure how he did hair, though) and without wasting a lot of water. (The ``gun'' could clean a family of four with *1 PINT* of water!) > >It's been impossible so far to find any information on the invention, because > all of the books I've found so far only deal with his major inventions, like > thegeodesic domes. Buckminster (so my lecturer tells me) came up with the idea > after observing some fishermen coming back after fishing in a fog. Their > hands, which should have been oily and dirty, were completely clean. He > hypothesised that the combination of fog and high wind had an efficient > cleaning effect. Actually it was Fuller himself who made the obsevation. I don't know of any technical specs for the device, but it's mentioned three times in the index to Fuller's _Critical_Path_. > >He invented a device that forced water through a nozzle to create a fine mist, > and a heating device was located at the junction between the hose and nozzle. Is this REALLY how he atomized the water? Has your instructor seen drawings? Has anyone seen drawings? I'm sure someone here has "The artifacts of R. Buckminster Fuller : a comprehensive collection of his designs and drawings" which may have details on this. I don't have this book :( > >This is all I know, and I don't know how acurate it is. Can anyone supply me > with more information? I hope this helps. > >Thanks, > >Jennifer > >jlmarang@acacia.itd.uts.edu.au -- Christopher J. Fearnley | UNIX SIG Leader at PACS cfearnl@pacs.pha.pa.us | (Philadelphia Area Computer Society) fearnlcj@duvm.bitnet | Design Science Revolutionary fearnlcj@duvm.ocs.drexel.edu | Explorer in Universe 503 S 44th ST | Linux Advocate Philadelphia PA 1914-3907 | (215)349-9681 ========================================================================= Date: Thu, 18 Aug 1994 23:21:51 -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: Kirby >In Article >Chris Fearnley writes: >>On Sat, 6 Aug 1994 14:38:00 GMT said: >>>Hey, whatever happened to Kirby? >>He posted that he was going to Africa with his family for a few weeks(?) >>He'll be back soon - judging from history he'll reply to all of the >>messages he has "missed." > >On that note, where would I find the archives? > Steve Mather > > Yeah, well, I'll definitely reply to this one at least. Yes, back from Africa -- Lesotho to be precise, where I read in the London Times this morning (still jet lagged) a coup has just taken place. So now I'm wondering about dad (mom's at a conference in New Mexico). I'm about to email the US Embassy there. Been looking over the PI thread. My software wimps out at 30 iterations but I'm confidant my algorithm was correct. Using pythagoras and the unit circle was all the rage for awhile, but in later decades, other methods have superceded. That quote from Kiyoshi awhile back about someone in the New York Times questioning the "actuality" of PI beyond a certain number of decimals (because nature is finite, not infinite), seems the way to connect back more directly to synergetics. So, yes, I'm out of Africa. Glad to be back with y'all. -- Kirby ------------------------------------------------ Kirby T. Urner pdx4d@teleport.com 4D Solutions (teleport.com is a public access node) ========================================================================= Date: Fri, 19 Aug 1994 02:47:40 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: Re: Kirby In-Reply-To: Message of Thu, 18 Aug 1994 23:21:51 -0700 from On Thu, 18 Aug 1994 23:21:51 -0700 Kirby Urner said: > >So, yes, I'm out of Africa. Glad to be back with y'all. Welcome Back. > >-- Kirby > >------------------------------------------------ >Kirby T. Urner pdx4d@teleport.com >4D Solutions (teleport.com is a public access node) ========================================================================= Date: Fri, 19 Aug 1994 22:14:33 EST Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "j.marang-acacia-dsn-student-91093738" Subject: I just went through those books today! In-Reply-To: <9408190625.AA18768@acacia.itd.uts.EDU.AU>; from "Chris Fearnley" at Aug 19, 94 02:10:42 am Hi again, Thanks Chris for the info! I had actually looked through the four volumes of the collection 'The artifacts of Buckminster Fuller;...' and they were very comprehensive - but only on his more reknowned inventions - with no mention of the fog gun. They are very good books though, because they are almost totally made up of his drawings, both engineering and sketchy concepts, of his inventions. Unfortunately, they seem very hard to get a hold of: at the library of my Uni, the books were located in the basement, and were not normally allowed for student viewing. Don't know why... Anyway, thanks again, and if there's anything else anyone knows I'm still interested! Jennifer jlmarang@acacia.itd.uts.edu.au ========================================================================= Date: Fri, 19 Aug 1994 10:10:27 EST/EDT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: DAMICO@GELMAN.CIRC.GWU.EDU Subject: Re: Fog Gun anyone? > On Fri, 19 Aug 1994 14:49:53 EST j.marang-acacia-dsn-student-91093738 said: > >Hi! > > > >I just popped onto this list in the hope that someone here could give me some > > information on an invention of Buckminster's known as a 'Fog Gun'. A lecture r > > ofmine told me about this invention and he used that name, so I hope it's > > right. > [Chris] > Here is what I've compiled on the fog gun from the FAQ: > Pat Salsbury originally posted the following: > The ``fog gun'' was an invention Bucky developed as a water saving > alternative to the wastefulness of showers. While Bucky was in the > navy, he noted that, while standing on the deck of a ship, in the spray > and mist of the sea, nothing seems to stay on your skin for very long. > Not even grease. He reasoned that it must have something to do with the > abrasive action of the tiny water droplets, so he developed a device > that atomized the water (like a perfume bottle with the little bulb that > you squeeze to get perfume mist) and ejected it at high speed. He dubbed > this the ``fog gun'' and found that it worked very well for cleaning a > person off without soap (I'm not sure how he did hair, though) and > without wasting a lot of water. (The ``gun'' could clean a family of four > with *1 PINT* of water!) > > > >It's been impossible so far to find any information on the invention, because > > all of the books I've found so far only deal with his major inventions, like > > thegeodesic domes. Buckminster (so my lecturer tells me) came up with the id ea > > after observing some fishermen coming back after fishing in a fog. Their > > hands, which should have been oily and dirty, were completely clean. He > > hypothesised that the combination of fog and high wind had an efficient > > cleaning effect. > > Actually it was Fuller himself who made the obsevation. I don't know of any > technical specs for the device, but it's mentioned three times in the index > to Fuller's _Critical_Path_. > > > >He invented a device that forced water through a nozzle to create a fine mist , > > and a heating device was located at the junction between the hose and nozzle . > > Is this REALLY how he atomized the water? Has your instructor seen drawings? > Has anyone seen drawings? I'm sure someone here has "The artifacts of R. > Buckminster Fuller : a comprehensive collection of his designs and drawings" > which may have details on this. I don't have this book :( > > I'll ask Ed to let me look at his copy of "artifacts". I intend to install these in my retirement home and I will be working with prototypes at my current home. It seems to me that the device (which Bucky did prototype) synergized the water pressure with an air compressor. A mixing valve would cause the air to draw the water through a (or several?) pinhole exit point(s). This would cause the fog to occur. The compressed air would be analogous to the bulb of air in the atomizer. As Fuller might say, that's "Everything I Know" about the fog gun. When I learn more, I will share it. "Just call me Trimtab" {~~~| R. Buckminster Fuller ~~~| _______ | / \ | BDAMICO@GWUVM.GWU.EDU ___________/__________\______|_____ \ Trimtab: A tiny gear / Blaine A. D'Amico |\ which moves the rudder / Systems Specialist ~~~~~~ |__\ that turns great ships / ~~~~~ Design Science Revolutionary --------------------- Comprehensive Generalist ========================================================================= Date: Fri, 19 Aug 1994 10:12:11 EST/EDT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: DAMICO@GELMAN.CIRC.GWU.EDU Subject: Re: Kirby > On Thu, 18 Aug 1994 23:21:51 -0700 Kirby Urner said: > > > >So, yes, I'm out of Africa. Glad to be back with y'all. > > Welcome Back. > > > >-- Kirby > > > >------------------------------------------------ > >Kirby T. Urner pdx4d@teleport.com > >4D Solutions (teleport.com is a public access node) > I'll be in Portland the week of the 29th. Can we meet on Wednesday afternoon? Would you like to come by our property and help plan our retirement dome? "Just call me Trimtab" {~~~| R. Buckminster Fuller ~~~| _______ | / \ | BDAMICO@GWUVM.GWU.EDU ___________/__________\______|_____ \ Trimtab: A tiny gear / Blaine A. D'Amico |\ which moves the rudder / Systems Specialist ~~~~~~ |__\ that turns great ships / ~~~~~ Design Science Revolutionary --------------------- Comprehensive Generalist ========================================================================= Date: Fri, 19 Aug 1994 22:01:33 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: quantum physics and tetrahedrons (x-post frm sci.math) I saw this on sci.math and thought I'd pass it along... Article: 75090 of sci.math Newsgroups: sci.physics.research,sci.math,sci.physics From: baez@ucrmath.ucr.edu (John Baez) Subject: This Week's Finds in Mathematical Physics (Week 38) Message-ID: <1994Aug19.204415.14387@galois.mit.edu> Originator: jbaez@euclid X-Sender: usenet@galois.mit.edu Nntp-Posting-Host: euclid Organization: MIT, Department of Mathematics Date: Fri, 19 Aug 94 20:44:15 GMT Approved: jbaez@math.mit.edu Lines: 303 This Week's Finds in Mathematical Physics (Week 38) John Baez I've been busy, and papers have been piling up; there are lots of interesting ones that I really should describe in detail, but I had better be terse and list them now, rather than waiting for the mythical day when I will have time to do them justice. So: 1) Topological quantum field theories from generalized 6j-symbols, B. Durhuus, H. P. Jakobsen and R. Nest, Reviews in Math. Physics 5 (1993), 1-67. In "week16" I explained a paper by Fukuma, Hosono and Kawai in which they obtained topological quantum field theories in 2 dimensions starting with a triangulation of a 2d surface. The theories were "topological" in the sense that the final answers one computed didn't depend on the triangulation. One can get between any two triangulations of a surface by using a sequence of the following two moves (and their inverses), called the (2,2) move: O O /|\ / \ / | \ / \ / | \ / \ O | O <----> O-------O \ | / \ / \ | / \ / \|/ \ / O O and the (3,1) move: O O /|\ / \ / | \ / \ / | \ / \ / | \ / \ / _O_ \ <----> / \ / _/ \_ \ / \ / _/ \_ \ / \ /_/ \_\ / \ O-----------------O O-----------------O Note that in either case these moves amount to replacing one part of the surface of a tetrahedron with the other part! In fact, similar moves work in any dimension, and they are often called the Pachner moves. The really *wonderful* thing is that these moves are also very significant from the point of view of algebra... and especially what I call "higher-dimensional algebra" (following Ronnie Brown), in which the distinction between algebra and topology is largely erased, or, one might say, revealed for the sham it always was. For example, as explained more carefully in "week16", the (2,2) move is really just the same as the *associative* law for multiplication. The idea is that we are in a 2-dimensional spacetime, and a triangle represents multiplication: two "incoming states" go in two sides and their product, the "outgoing state", pops out the third side: O / \ / \ / \ A B / \ / \ / \ / \ O--------AB-------O Then the (2,2) move represents associativity: O O /|\ / \ A | (AB)C A A(BC) / | \ / \ O AB O <----> O--BC---O \ | / \ / B | C B C \|/ \ / O O Of course, the distinction between "incoming" and "outgoing" sides of the triangle is conventional, and the more detailed explanation in "week16" shows how that fits into the formalism. Roughly speaking, what we have is not just any old algebra, but an algebra that, thought of as a vector space, is equipped with an isomorphism between it and its dual. This isomorphism allows us to forget whether we are coming or going, so to speak. Hmm, and here I was planning on being terse! Anyway, the still *more* interesting point is that when we think about 3-dimensional topology and "3-dimensional algebra," we should no longer think of O O /|\ / \ / | \ / \ / | \ / \ O | O and O-------O \ | / \ / \ | / \ / \|/ \ / O O as representing *equal* operations (the 3-fold multiplication of A, B, and C); instead, we should think of them as merely *isomorphic*, with the tetrahedron of which they are the front and back being the isomorphism. The basic philosophy is that in higher-dimensional algebra, as one ascends the ladder of dimensions, certain things which had been regarded as *equal* are revealed to be merely isomorphic. This gets tricky, since certain *isomorphisms* that were regarded as equal at one level are revealed to be merely isomorphic at the next level... leading us into a subtle world of isomorphisms between isomorphisms between isomorphisms... which the theory of n-categories attempts to systematize. (I should note, however, that in the particular case of associativity this business was worked out by Jim Stasheff quite a while back: it's the homotopy theorists who were the ones with the guts to deal with such issues first.) Now, it turns out that in 3-dimensional algebra, the isomorphism corresponding to the (2,2) move is not something marvelously obscure. It is in fact precisely what physicists call the "6j symbol", a gadget they've been using to study angular momentum in quantum mechanics for a long time! In quantum mechanics, the study of angular momentum is just the study of representations of the group SU(2), and if one has representations A, B, and C of this group (or any other), the tensor products (A tensor B) tensor C and A tensor (B tensor C) are not *equal*, but merely *isomorphic*. It should come as no surprise that this isomorphism is represented by physicists as a big gadget with 6 indices dangling on it, the "6j symbol". Quite a while back, Regge and Ponzano tried to cook up a theory of quantum gravity in 3 dimensions using the 6j symbols for SU(2). More recently, Turaev and Viro built a 3-dimensional topological quantum field theory using the 6j-symbols of the *quantum group* SU_q(2), and this led to lots of work, which the above article explains in a distilled sort of way. The original Ponzano-Regge and Turaev-Viro papers, and various other ones clarifying the relation of the Turaev/Viro theory to quantum gravity in spacetimes of dimension 3, are listed in "week16". It's also worth checking out the paper by Barrett and Foxon listed in "week24", as well as the following paper, for which I'll just quote the abstract: ...other not-related paper abstracts deleted... ========================================================================= Date: Thu, 18 Aug 1994 19:03:00 -0400 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: William Cringan Organization: CRS Online (Toronto, Ontario) Subject: flyer Please send me a flyer with the buckeyball kit. My address is: William Cringan, 2267 Westman Rd. Mississauga, Ontario. L5K 1M7 Thanks Kindly. --- * OLX 2.1 TD * All wiyht. Rho sritched mg kegtops awound? ========================================================================= Date: Sat, 20 Aug 1994 06:41:25 -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: flyer >Please send me a flyer with the buckeyball kit. >My address is: > >William Cringan, >2267 Westman Rd. >Mississauga, Ontario. >L5K 1M7 > >Thanks Kindly. > >--- > * OLX 2.1 TD * All wiyht. Rho sritched mg kegtops awound? > > The science toys company which produced a buckyball kit (some of which were sold through the Buckminster Fuller Institute) is: Mondotronics 524 San Anselmo Ave #107 San Anselmo, CA 94960 Phone 414-455-9330 Fax 414-455-9333 email mondo@holonet.net Its a small company run by Roger G. Gilbertson. Their most popular products feature "muscle wires" -- highly processed strands of nickel-titanium (nitinol) which stretch at room temperature but harden into their unstretched shapes when conducting an electrical current. The buckyball kit consists of four sheets of flexible plastic each containing 3 pentagons and 5 hexagons. You pop these out and snap them together edgewise to assemble a buckyball that's a bit smaller than a soccer ball. No glue or other materials required. The kit also comes with a booklet giving background information on buckyballs and even some synergetics. I was the author of the booklet (Roger and Celene designed and edited it). The information is still relevant, if a bit dated (hottest area of chemical research is going to obsolete its info quickly of course). I used a buckyball kit with 6th graders in Lesotho, Africa just about a week ago. We also assembled a vector flexor. The tensegritoy takes more time and will have to wait 'til another time. -- Kirby ------------------------------------------------ Kirby T. Urner pdx4d@teleport.com 4D Solutions (teleport.com is a public access node) ========================================================================= Date: Sat, 20 Aug 1994 23:50:01 -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: Geodesic Dome Software Can anyone tell me if there is any software out there to design geodesic domes with, and create different 2, 3, 4, 6, 8 frequency designs ?????????? please E-Mail me on America On Line at Grego10067, or on this forum, I will offer a reword leading to the purchase of this software, ========================================================================= Date: Sun, 21 Aug 1994 20:32:10 -0800 Reply-To: Curtis@dbug.org Sender: List for the discussion of Buckminster Fuller's works From: SimulatedSnow Organization: Baloney Research Institute Subject: Re: World Game In article <32bh68$k2u@dunx1.ocs.drexel.edu>, XTM00003@DUVM.OCS.DREXEL.EDU (Dane Winberg) wrote: | As for comments and experiences of past participants at the workshops, I look | forward to seeing them posted here. I've worked for WGI for 11 years... I attended a WG in the mid 70's & consider it one of the highlights of my life. The perspective stays w/me. I would like for all candidates for public office to be exposed to this...top to bottom. Any word on plans for next year ? | Dane Winberg | World Game Institute -Mahalo for the 11 years & the future ! -- -Planning for years, plant rice -Planning for decades, plant trees -Planning for centuries, educate people ========================================================================= Date: Mon, 22 Aug 1994 06:21:05 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: Fog Gun anyone? >From what I have, in Bucky's book "Critical Path", your description is fairly accurate. As a sidenote. We could sure do with some of Bucky's bathroom designs here in Auckland, New Zealand. We are in the grips of a water shortage and are all trying to save water. Now that I'm conscious of it, it has become obvious what a ridiculous amount of water each household uses. Regards Ross Keatinge icosa@iconz.co.nz ========================================================================= Date: Mon, 22 Aug 1994 08:38:56 -0600 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: "Bob Bayn, mgr. Academic Services, Computer Center" Subject: Re: Fog Gun anyone? >From: Ross Keatinge >As a sidenote. We could sure do with some of Bucky's bathroom designs here >in Auckland, New Zealand. We are in the grips of a water shortage and are >all trying to save water. Now that I'm conscious of it, it has become >obvious what a ridiculous amount of water each household uses. Utah's cronic water shortage is also acute this year. It's made me think that my dream of a geodesic dome home probably ought to include some facility for greywater capture and reuse (probably for irrigation). What the heck, my preliminary investigations suggest that planners, inspectors and lenders are all going to be hard sells for my efforts, I may as well hit 'em with non-conforming plumbing, too. Unfortunately, I haven't a clue as to where to find info about workable greywater collection systems in new construction. I don't believe that Bucky did any design work on this topic. Anybody know of any specs, layouts or designs that would complement Bucky's dome? -- Robert Bayn http://happy.usu.edu/~bob/index.html o bob@cc.usu.edu I just can't picture having \__^\=* Logan, Utah, USA fun by burning gas. (O)""""o ========================================================================= Date: Mon, 22 Aug 1994 10:41:35 GMT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Tom Buckley Organization: NB*Net Subject: stress analysis Can anyone tell me how to get some software or otherwise so that I can determine the stresses on dome members? ********************************************************* * TERRAIN ENGINEERING LTD. * *P.O. Box 2703,Saint John, New Brunswick,CANADA E2L 4Z1* * * * voice, fax: 506-832-4929 * * 14400 or less, N81, Zmodem (ask) * ********************************************************* ========================================================================= Date: Mon, 22 Aug 1994 11:09:47 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Bob Cook Subject: Solar Village Questionaire Tucson Solar Village Thank you for your help in planning Phase 3 of the Tucson Solar Village Program. We were pleased with the quality and thoughtfulness of the responses to the first cycle. In this second cycle Delphi process we will review responses from the first cycle, try to identify the most important issues and examine them further. This second questionnaire is intended to be somewhat more specific than the first. We encourage you to add ideas and suggestions to those listed. The final questionnaire will incorporate responses from this and the first one and will become more detailed and specific. It is important that you mail or fax your responses in time to be received by Monday, August 29, 1994 to: Robert Cook, Solar Village Committee Chair Tucson-Pima County Metropolitan Energy Commission BCOOK@Pimacc.Pima.Edu FAX (602) 748-4754 Phone (602) 748-4745 Thank you again for your participation. In this second cycle of the Delphi process, we complete responses to the first cycle for each of the main issues. Now, would you please review these lists and help make them as complete as possible by adding important items that have not been mentioned so far. Then, we ask that you select the 3-5 most important items and explain briefly why they are important. The explanations are important to the process, so please give them careful consideration. Finally, we ask for your creative help with two questions that are of particular concern at this time. Thank you again for your help. 1. Following is a list of important features in Civano cited by respondents. Please add any others you think should be listed, then select 3-5 features by letter reference that you feel are most important, and explain why. a. Passive solar design b. Photovoltaic generation system c. Pedestrian path system d. Resource conservation area e. Bicycle path system f. Connection to public transportation g. Neighborhoods to support design flexibility h. Diverse socio-economic inclusion i. Sense of neighborhood & place j. Community & on-site water harvesting k. Neighborhood social & recreation centers l. Clustered building layout with open space m. Access to regional trails system n. Proximity to on-site jobs o. Walkable village center p. Community education program q. Recycling options r. Community gardens, orchards s. Reclaimed effluent system t. Community tram system u. Other: v. Other: Letter Why important 2. Following is a list of activities cited by respondents as important to assure the successful development of Civano. Please add any others you think should be listed, then select 3-5 activities which you think are most important, and explain why. a. Offer competitive home value b. Involve associations, groups & individuals c. Provide incentives for developers d. Integrate environmental education e. Build demonstration program now f. Build office work stations in each home g. Use best minds of designers & engineers h. Attract a sympathetic developer i. Establish a Community Resource Center j Form management/overseeing body now k. Prepare focused market analysis/strategy l. Conduct public info/relations program m. Integrate with community revitalization n. Define photovoltaic program with TEP o. Redefine land sale to include all values p. Committed people on design review q. Prepare strong agency commitments r. Structural efficiencies built into all phases s. Include range of uses in all phases t. Seek additional resources to assure goals u. Build village center & plaza early v. Screen buyers for "Civano" values w. Other: x. Other: Letter Why important 3. Following is a list of Civano aspects cited by respondents as important to implement in the community at large. Please add any others you think should be listed, then select 3-5 activities/projects which you think are most important, and explain why. a. Develop Civano concepts as infill project b. Solar: water heat, passive design, solar thermal, pv systems c. Preserve wash habitat corridors d. Target areas for ped-friendly design e. Education re sustain. design principles f. Ped access to neighborhood nodes g. Focus on getting Civano built as demo h. Awards program for exceeding targets i. Apply Civano performance targets to all j. More affordable housing options k. More trees & shade l. Provide bicycle-friendly design features m. Pedestrian emphasis throughout region n. Energy conserv'n equipment, techniques o. Water conserv'n equipment, techniques p. Recycling to the max q. Document existing local examples r. Build infill demonstration housing s. Alternative transportation corridors t. Other: u. Other Letter Why important 4. Following is a list of ways cited by respondents to bring the best people with the right resources together to get the job done. Please add any others you think should be listed, then select 3-5 ways which you feel are most important, and explain why. a. Let a committed developer manage it b. Secure interest of Fortune 500 company c. Form public-private-nonprofit partnership d. Continue getting the word out e. Network with inclusive stakeholder groups f. Develop a management association g. Advertise nationally for "right" developer h. Aggressive leadership & management i. Leverage funding: seek additional grants j. Task forces to deal with important aspects k. Continue doing what MEC is now doing. l. Support full time staff to ensure continuity m. Consider each retailer, employer, resident as stockholder n. Let the successful land purchaser manage it o. Convince larger public of economic viability p. Other: q. Other: Letter Why important 5. Many of the respondents to the first questionnaire suggested that marketing techniques and economic feasibility analyses of specific features in Civano are very important in assuring its successful development. If you were the enlightened sales manager for the Civano developer, what would be the elements of your marketing strategy? 6. Many respondents to the first questionnaire felt that leadership and developing partnerships and cooperation between builders, developers, public agencies, civic organizations and utility/service providers is critical to developing the Solar Village Program. What would be the best way(s) to form such public/private partnership(s) or cooperation? 7. Many respondents to the first questionnaire felt that there should be a set of developer incentives to encourage conformance with the Civano goals and objectives. What kinds of incentives do you think would be appropriate to assure inclusion of the following features. FEATURES INCENTIVES Clustered housing with open space around Village commercial center to begin with Village & neighborhood social centers Separate bicycle and pedestrian paths Natural open space & drainage preservation Jobs creation within Civano Create personal office setup in home Photovoltaic generating system Community education program Community gardens, orchards Co-housing options "Sweat equity" housing options Low-income housing options Connection to public transit alternatives Recycling of materials 8. Please feel free to add any other comments/ideas/suggestions which you think would further the implementation of Civano and encourage the development of related projects throughout the community, or comments on the questionnaires thus far. Robert Cook, Solar Village Committee Chair Tucson-Pima County Metropolitan Energy Commission BCOOK@Pimacc.Pima.Edu FAX (602) 748-4754 Phone (602) 748-4745 Again, thank you for your participation. ========================================================================= Date: Mon, 22 Aug 1994 14:29:56 EST/EDT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: DAMICO@GELMAN.CIRC.GWU.EDU Subject: Re: Fog Gun anyone? > > >From: Ross Keatinge > >As a sidenote. We could sure do with some of Bucky's bathroom designs here > >in Auckland, New Zealand. We are in the grips of a water shortage and are > >all trying to save water. Now that I'm conscious of it, it has become > >obvious what a ridiculous amount of water each household uses. > > Utah's cronic water shortage is also acute this year. It's made me > think that my dream of a geodesic dome home probably ought to include > some facility for greywater capture and reuse (probably for irrigation). > What the heck, my preliminary investigations suggest that planners, > inspectors and lenders are all going to be hard sells for my efforts, > I may as well hit 'em with non-conforming plumbing, too. Unfortunately, > I haven't a clue as to where to find info about workable greywater > collection systems in new construction. I don't believe that Bucky > did any design work on this topic. Anybody know of any specs, layouts > or designs that would complement Bucky's dome? > -- > Robert Bayn http://happy.usu.edu/~bob/index.html o > bob@cc.usu.edu I just can't picture having \__^\=* > Logan, Utah, USA fun by burning gas. (O)""""o > Actually, Bucky focused on not creating as much grey water to start with. Along with the fog gun was the dry toilet which Bucky proposed. Bucky wanted us to stop taking the waste products that nature has so carefully seperated into liquid and solid and mix them up again in order to dispose of them. He proposed a toilet that plastic wrapped dry waste in hermetically sealed packages. Solid waste could then be converted into energy at the homesite or trucked away to third party energy plants. Dont' know about any gery water projects that Bucky did. "Just call me Trimtab" {~~~| R. Buckminster Fuller ~~~| _______ | / \ | BDAMICO@GWUVM.GWU.EDU ___________/__________\______|_____ \ Trimtab: A tiny gear / Blaine A. D'Amico |\ which moves the rudder / Systems Specialist ~~~~~~ |__\ that turns great ships / ~~~~~ Design Science Revolutionary --------------------- Comprehensive Generalist ========================================================================= Date: Mon, 22 Aug 1994 15:40:50 -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: Fog Gun anyone? Robert Bayn wrote: >Utah's cronic water shortage is also acute this year. It's made me >think that my dream of a geodesic dome home probably ought to include >some facility for greywater capture and reuse (probably for irrigation). >[snip] >Anybody know of any specs, layouts or designs that would complement >Bucky's dome? I was considering the problem recently and decided that a solar powered evaporator/condenser would be worth looking into. Such a device would produce recycled water of sufficient quality for drinking. I don't have any plans, but I'll describe what I had in mind: - a greywater tank within a passive, solar collector box; - pipes carry the water vapor from the tank through a trough of cold water, where it condenses back into liquid. The trough is chilled by the solid state cooling devices they use on those new portable ice-chests you plug into your car's cigarette lighter [sorry, I've forgotten their name]) =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= Lee Wood | Lee_Wood@sfu.ca | INTJ spoken here. =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= ========================================================================= Date: Mon, 22 Aug 1994 23:29:27 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: Re: stress analysis In-Reply-To: Message of Mon, 22 Aug 1994 10:41:35 GMT from On Mon, 22 Aug 1994 10:41:35 GMT Tom Buckley said: >Can anyone tell me how to get some software or otherwise so that I can >determine the stresses on dome members? FElt 2.0 is availble for Unix systems (binary releases for Linux, HP-UX and SUNOS). It is a finite element analysis package. Although I haven't played with it yet, it seems like a good package for simple structural analysis. Robert L. Read reported on this group awhile ago "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. It can handle lots of stuff (hence "Finite Element") but of particular interest to fans of Fuller is that it easily handles "tensegrity" structures, where a tensegrity structures is one in which force is transmitted only axially along members (cables or struts)." It is copylefted software (GPL) and 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. >********************************************************* >* TERRAIN ENGINEERING LTD. * >*P.O. Box 2703,Saint John, New Brunswick,CANADA E2L 4Z1* >* * >* voice, fax: 506-832-4929 * >* 14400 or less, N81, Zmodem (ask) * >********************************************************* -- Christopher J. Fearnley | UNIX SIG Leader at PACS cfearnl@pacs.pha.pa.us | (Philadelphia Area Computer Society) fearnlcj@duvm.bitnet | Design Science Revolutionary fearnlcj@duvm.ocs.drexel.edu | Explorer in Universe 503 S 44th ST | Linux Advocate Philadelphia PA 1914-3907 | (215)349-9681 ========================================================================= Date: Tue, 23 Aug 1994 02:34:28 EDT Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Postmaster Subject: Re: Fog Gun anyone? Sorry for jumping in it so abruptly. I think those solid sate cooling devices consumes a lot of energy. It may be a problem with a PV system. Also, they are based on a principle named the "Pelletier effect". I find your project very interesting. Don't give up! Marc Tremblay, marc@harfang.login.qc.ca ========================================================================= Date: Tue, 23 Aug 1994 07:43:33 -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: stress analysis X-cc: rich@cpp.pha.pa.us In-Reply-To: from "Chris Fearnley" at Aug 22, 94 11:29:27 pm Chris: Even if only axial stresses are measured in a pure tensegrity structure rather than a dome with multiple nodes, the stress analysis of dome members is still far too complex to compute with any existing software. Fuller compared such an analysis with analyzing the movement of all the air molecules in a basketball simultaneously. For that reason, structurl engineers were forced by this to test geodesic structures by loading them to failure. Because of this fact, geodesic domes were often greatly overbuilt because of the need for conservativism, since the mathematical tools were not and still are not available. --Kiyoshi Quoted message begins here: > > On Mon, 22 Aug 1994 10:41:35 GMT Tom Buckley said: > >Can anyone tell me how to get some software or otherwise so that I can > >determine the stresses on dome members? > > FElt 2.0 is availble for Unix systems (binary releases for Linux, HP-UX and > SUNOS). It is a finite element analysis package. Although I haven't > played with it yet, it seems like a good package for simple structural > analysis. Robert L. Read reported on this group awhile ago > > "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. It can handle lots of stuff (hence > "Finite Element") but of particular interest to fans of Fuller is that > it easily handles "tensegrity" structures, where a tensegrity structures > is one in which force is transmitted only axially along members (cables > or struts)." > > It is copylefted software (GPL) and 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. > > >********************************************************* > >* TERRAIN ENGINEERING LTD. * > >*P.O. Box 2703,Saint John, New Brunswick,CANADA E2L 4Z1* > >* * > >* voice, fax: 506-832-4929 * > >* 14400 or less, N81, Zmodem (ask) * > >********************************************************* > -- > Christopher J. Fearnley | UNIX SIG Leader at PACS > cfearnl@pacs.pha.pa.us | (Philadelphia Area Computer Society) > fearnlcj@duvm.bitnet | Design Science Revolutionary > fearnlcj@duvm.ocs.drexel.edu | Explorer in Universe > 503 S 44th ST | Linux Advocate > Philadelphia PA 1914-3907 | (215)349-9681 > ========================================================================= Date: Tue, 23 Aug 1994 08:17:40 -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: Greywater Recycling (was: Fog Gun anyone?) Marc Tremblay wrote: > I think those solid sate cooling devices >consumes a lot of energy.[snip] Also, they >are based on a principle named the "Pelletier effect". Right, "Pelletier Effect Devices", thank you. As for the power consumption question, I will plead ignorance. It was not one of my design concerns. In fact, I had only two main design considerations: 1 - I started from the premise that water was an extremely valuable resource and that water recycling would be mandatory, irrespective of cost. 2 - I was designing for a solar power source, so once installed, the electricity would "free". On the plus side, when based on a photo-voltaic/battery electrical supply, the entire system would have NO moving parts. So, compared to a refrigerator, which has MANY moving parts, AS WELL AS high power consumption, this system *should* have a longer life and be essentially maintenance free. Two final notes: 1 - Evaporative cooling was not an option, since it wastes water. 2 - The CAPS are not intended to indicate "shouting" i.e. a FLAME response. They are merely for emphasis. =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= Lee Wood | Lee_Wood@sfu.ca | INTJ spoken here. =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= ========================================================================= Date: Tue, 23 Aug 1994 12:39:36 -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: Dome for Taj Mahal? Hello, I caught an article in our local paper over the weekend saying that a lawyer in the Agra region of India has begun circulating a petition to get over 8000 factories moved out of the area as a means of preserving the Taj Mahal from the effects of pollution. This made me wonder if building a large geodesic structure to enclose the building and then controlling the atmosphere within the dome wouldn't be easier (and cheaper and a more permanent solution) than trying to displace that much industry. Think a structure that large could handle the stress of its own weight? Anyone on this forum who lives in that area that would be interested in forwarding this idea to local planners? To me a dome of this size would be almost as incredible a feat as the construction of the Taj Mahal itself. Anyone know about how large such a dome would have to be? Enough questions...thanx for your time. Bill Long >-- StarGazer ========================================================================= Date: Tue, 23 Aug 1994 12:48:18 -0700 Reply-To: List for the discussion of Buckminster Fuller's works Sender: List for the discussion of Buckminster Fuller's works From: Mark Phillips Subject: Re: Greywater Recycling (was: Fog Gun anyone?) In-Reply-To: <9408231517.AA17624@rain.org> I am also looking into using these thermoelectric cooling devices (Peltier device) in conjunction with a solar electric source. On the surface, these devices seem to be pretty good, no moving parts, 12 VDC operation, low power (ie. 3 A @ 12VDC for 36 watts), no freon or other working fluid, quiet. But I've talked to several people, including one from a peltier device manufacturer that have tried to tell that they are not good for refrig/freezers. Part of the problems are: - they usually do need two fans (like in the back of your computer) to transfer the heat to/from the cold/heat sinks. - There are compressors out there optimized for 12VDC operation that are efficient with power consumption. - It seems that a single device only brings the internal temperature down to 41 deg F. Well above freezing. And that temperature is dependent on what the ambient temperature is. With all that, I am not daunted but and am a little more wary and not quite as excited or optimistic. You can cascade (use 2 devices back to back) for a larger temperature drop. And I still think the devices might be more reliable and have a longer life. It is just going to be a larger engineering design challenge. These companies manufacture Peltier devices and if you contact them, they will send you there literature complete with applications guides, product desc. and price lists: MELCOR 1040 Spruce St Trenton NJ 08648 609-393-4178 MARLOW INDUSTRIES 10451 Vista Park Rd Dallas, TX 75238 214-340-4900 SUPERCOOL US PO DRAWER 9066 San Rafeal, CA 94912 415-459-3777 Also check the Thomas register under Cooling, Thermoelectric devices or Thermoelectric cooling devices. I hope this helps you and doesn't discourage you. If it was easy, it would have been done by now, but that doesn't mean it's impossible. Good luck and good designing. ========================================================================= Date: Wed, 24 Aug 1994 09:15:45 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: Alpha, Beta, Hexagonal closest packing I have a question that no one I know can answer. Why is the alpha state of crystals usually weaker than the beta state? Is it because the beta state makes a more efficient use of materials (i.e. is less dense,) or what? Steve Mather ========================================================================= Date: Wed, 24 Aug 1994 17:51:45 -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: The "PI without Trig" Monster Returns SUBJECT: The "PI without Trig" Monster Returns 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: As you may recall, a few weeks ago we discussed an algorithm for determining PI without using trig. [The algorithm divided a circle (radius=1) into smaller and smaller right triangles, each of whose hypotenuse lay progressively closer to the circumference of the circle. The hypotenuse was of a known length, and was an integer fraction of the circumference of the circle, so we could then calculate a good approximation for the length of the actual circumference. Knowing the radius and circumference, we could then determine PI to a fair degree of accuracy.] Well, I decided to apply a similar technique to finding the volume of a sphere (also of radius 1). My algorithm filled the sphere with flat cylinders (more like hockey pucks, actually), all contained (mostly) within the surface of the sphere. I then calculated the volume for each cylinder, and obtained their sum. NB actually, I filled only the upper hemisphere with cyl