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Conference rusure::math

Title:	Mathematics at DEC

Moderator:	RUSURE::EDP

Created:	Mon Feb 03 1986
Last Modified:	Fri Jun 06 1997
Last Successful Update:	Fri Jun 06 1997
Number of topics:	2083
Total number of notes:	14613

1475.0. "Sphere Packing" by JARETH::EDP (Always mount a scratch monkey.) Thu Aug 01 1991 17:26

Article 19604 of sci.math:
Path: nntpd.lkg.dec.com!rust.zso.dec.com!pa.dec.com!decwrl!uunet!spool.mu.edu!mips!ultra!jimh
From: [email protected] (Jim Hurley)
Newsgroups: sci.math
Subject: Packing Problem solved - summary?
Message-ID: <[email protected]>
Date: 31 Jul 91 16:55:04 GMT
Organization: Ultra Network Technologies
Lines: 11

I just read that the sphere packing problem in 3 dimensions
has been proven and that the proof is being circulated.

Could someone kindly give a history of the problem and
why it has been so difficult to prove?

The article stated that a whole new area of spherical geometry had to be
developed. 
-- 
Jim Hurley --> [email protected]  ...!ames!ultra!jimh  (408) 922-0100
Ultra Network Technologies / 101 Daggett Drive / San Jose CA 95134

T.R	Title	User	Personal Name	Date	Lines
1475.1	Tennis, anyone?	CIVAGE::LYNN	Lynn Yarbrough @WNP DTN 427-5663	`Thu Aug 01 1991 18:07`	11
	The sphere packing problem is related to the following 2-dimensional problems: a) How many unit circles can be placed tangent to a given unit circle? b) What is the 2D packing density of unit circles? The answer in both cases is 6. In 3-D the problem is more difficult. The answer has been known to be 'between 12 and 13' for a long time, but no one has been able to prove that 13 is not possible (until, apparently, now). The practical application is that it defines the maximum packing density for things shaped like spheres, e.g. ping-pong balls.
1475.2	Tangentially speaking	VMSDEV::HALLYB	The Smart Money was on Goliath	`Thu Aug 01 1991 19:02`	6
	I wonder if this problem has applications in the chemistry (physics?) field of "buckyballs" -- near spherical molecules of carbon, 60 or more atoms to the molecule, arranged in geodesic spheres. Cheap and easy to make. John
1475.3	soccerball example?	CIVAGE::LYNN	Lynn Yarbrough @WNP DTN 427-5663	`Wed Aug 14 1991 13:16`	6
	Perhaps. Right now I can't find it, but I recall seeing a theorem to the effect that (and I'm really stretching my memory) a geodesic sphere made up of pentagons and hexagons must have exactly 12 pentagons. The degenerate case of this is the dodecahedron, and I'm not sure if there is an upper limit on the number of hexagons. Someone have a soccerball handy? I think it has one hexagon between each pair of pentagons.