In Oct 98, in the magazine Nature, Neil A. Sloane of AT&T Research
stated that Buckminster Fuller claimed a proof of the famous Kepler's
Conjecture in his book Synergetics, back in 1975. To quote Sloane in
detail:

   "Buckminster Fuller claimed to have a proof in 1975, but his
   arguments amount to a description of the face-centred-cubic
   packing rather than a proof of it minimality".

You can see the article here: http://www.research.att.com/~njas/doc/kepler.pdf

The question is: Where in the book, does Fuller makes the claim ?
Details, please, page and line numbers.

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Request for Question Clarification by markj-ga on 18 Mar 2004 08:31 PST

pauloney --

I expect to be able to give you a complete citation  to the material
that interests you -- page(s), lines, publisher, publication date --
by sometime this afternoon. Would that be a sufficiently "detailed"
answer to your question?

markj-ga

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Clarification of Question by pauloney-ga on 18 Mar 2004 11:25 PST

I do have the publication which is:

   Fuller, R. Buckminster (Richard Buckminster), 1895- 
   Synergetics; explorations in the geometry of thinking [by] R. Buckminster
   Fuller in collaboration with E. J. Applewhite. Pref. and contribution by
   Arthur L. Loeb, New York, Macmillan (1975)

All that I need is the location in the book where the claim occurs.

Paulo Ney

Look at section numbers 222.00 - 222.53. I think you'll find the answer there. 

Saikiran

I have been there many times, and just went back and re-read all the
pages, you suggested and sure not, I can't see a place where he claims
to have the proof of the result in there. I see he using the result,
but no claim of a proof ... so try harder, or if you know where it is,
send me the page and the line where the claim is made.

Paulo de Souza

saikiran --

I'm sorry for possibly raising your expectations of a quick answer
from me.  I assumed that you didn't have access to the book and that a
layman could find what you are seeking with the help of a good index
and some facility in visually scanning a text. I now see that this
large book has no index and is geared to readers more mathematically
literate than I.

I hope that another researcher can help you.

markj-ga

pauloney -- I apologize for confusing your screen name with that of
the commenter in this thread.

markj-ga

pauloney --

I have found some information that might be very useful to you,
although I do not have the mathematical background to evaluate it. 
Below is a link to an Amazon.com page related to a book called
"Kepler's Conjecture: How Some of the Greatest Minds in History Helped
Solve One of the Oldest Math Problems in the World,"  by George G.
Szpiro.

You may be aware that Amazon.com now offers a search feature that
allows one to look for references to specified search terms in the
text of certain books in its inventory.  I employed such a search of
the Amazon.com site using the terms "Kepler Conjecture" and "Fuller." 
Among the results was an excerpt from the Szpiro book that provides an
enlightening discussion of Buckminster Fuller's "claim" of proving the
Kepler Conjecture in his book, "Synergetics."

You should be taken to the first page of the excerpt by clicking on this link:

http://www.amazon.com/gp/reader/0471086010/ref=sib_vae_pg_141/002-4020173-6346469?%5Fencoding=UTF8&keywords=fuller&p=S049&twc=14&checkSum=eJum8B515sDFi2OC1H95OtA0JqThh1fpQ6c40oRShps%3D#reader-link

The relevant excerpt continues for several pages, which you can access
by clicking on "Next Page."

I do not have the background to evaluate this discussion, but you may
find it useful,and indeed it may answer your question.  In essence,
Szpiro concludes that Fuller merely repackaged old ideas and invented
new terms without breaking any new ground.  Fuller's "repackaging" of
the problem may explain why there is no express "claim" and indeed no
mention of Kepler, as far as I can determine.

Szpiro says that the references of the "packing of spheres" are
scattered throughout the  book, but it appears that much of Fuller's
discussion of the topic is concentrated in Sections 410-420, beginning
on page 108 of Synergetics.

If you have any problem with the long URL I have provided, please let
me know and I will walk you through the process of conducting your own
search.

I hope this information helps you.  If you believe that this research
has answered your question, I would be happy to post the information
in the "Answer" box.

markj-ga

MarkJ, I agree with you that this is yet another quote that Fuller
claimed the proof of the Kepler conjecture (or closest packing in
Fuller's words) but there is very good indication that Szpiro is just
"repeating" what Neil Sloane said in the aforementioned publication
... and we still don't have the Holy Grail that is - where did Fuller
make such claim ? If he ever made it ...