Bounds on the kissing number
- From: jankrihau@xxxxxxxxxxx
- Date: Wed, 14 Nov 2007 23:46:59 -0800 (PST)
Let k(n) denote the kissing number in n dimensions, i.e., the maximal
number of hyperspheres of radius 1 that can touch a given hypersphere
of radius 1 without any overlapping. I am interested in bounds on a =
lim k(n)^(1/n), but the information I have managed to find on the net
is somewhat limited.
The page http://cherrypit.princeton.edu/sphd/ mentions a lower bound
2^0.2075... which is probably (?) a re-writing of 2 / sqrt(3). I have
not seen any upper bounds.
Numerical evidence might suggest a = something near sqrt(2); the
formula 2n (2^(n/2) - 1) actually gives the exact kissing number for
the exceptional cases n = 8 and n = 24, but it is not quite right for
n = 2 and 3. (And I am not overly excited about its apparent
correctness for n = 4 since an arrangement of 24 hyperspheres around a
given one leaves a lot of "extra room".) However, I have a heuristic
argument that indeed points towards an upper bound of sqrt(2) for a.
Is this an already proven upper bound?
Thanks in advance.
---
J K Haugland
http://home.no.net/zamunda
.
- Follow-Ups:
- Re: Bounds on the kissing number
- From: Michael Press
- Re: Bounds on the kissing number
- Prev by Date: Re: make 100 by using 1, 7, 7, 7, 7
- Next by Date: Re: Lattice visualization tool
- Previous by thread: I am a good teacher of math if need for help contact me
- Next by thread: Re: Bounds on the kissing number
- Index(es):
Relevant Pages
|
