6 Mar
2008
6 Mar
'08
10:11 p.m.
On 3/5/08, Ed Pegg Jr <ed@mathpuzzle.com> wrote:
I was recently looking at a beautiful Kissing Spheres page:
http://pagesperso-orange.fr/math-a-mater/pack/packing.htm
About halfway down the page, there is a simple question: Five colors suffice ? Interesting question.
Consider the natural way to generate the tiling: start with a large (outer) sphere with three tangent spheres inside; then at each generation place a new smaller sphere within every pre-exisiting cavity. Each new sphere is tangent to just four larger ones; therefore it may be coloured using the fifth colour. A similar argument shows that n+2 colours suffice in n-space. WFL