26 Sep
2003
26 Sep
'03
10:21 a.m.
----- Original Message ----- From: "John Conway" <conway@Math.Princeton.EDU> To: "math-fun" <math-fun@mailman.xmission.com> Sent: Friday, September 26, 2003 8:35 AM Subject: Re: [math-fun] Re: Kissing number.
Similarly, a unit sphere kissing unit sphere S "uses up" an area A of the surface of C subsumed by a circle with a 60-degree diameter, so that NL(3) <= (4pi)/A. Does this observation generalize to higher dimensions?
Yes of course, but it only gives the bound 13 in 3 dimensions.
In "Kepler's Conjecture" by George Szpiro, it says that the naive angle-occupying calculation in 3-D gives an absolute upper bound of 14.9 spheres. This is just a solid-angle calculation. This should be easy to recompute by hand.