Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10 5/3/83; site eosp1.UUCP Path: utzoo!linus!decvax!harpo!ulysses!princeton!eosp1!mcmillan From: mcmillan@eosp1.UUCP (John McMillan) Newsgroups: net.ai Subject: Re: Four color... Message-ID: <596@eosp1.UUCP> Date: Fri, 17-Feb-84 15:33:24 EST Article-I.D.: eosp1.596 Posted: Fri Feb 17 15:33:24 1984 Date-Received: Tue, 21-Feb-84 04:39:27 EST References: <5540@uiucdcs.UUCP> <1290@mit-eddie.UUCP> Organization: Exxon Office Systems, Princeton, NJ Lines: 17 It was proved long ago that 7 colors suffices for a Torus. I believe that a sphere cannot require more colors than a plane. The proofof this (?) is as follows: You can convert a sphere into a plane by piercing a hole in it the size of a point, and then stretching it out flat. In a colored map, no countries meet at a point; they must share a border that has some length. Therfore piercing a hole in a spherical map does not change any of its boundary conditions, while converting it into a plane. - Toby Robison allegra!eosp1!robison decvax!ittvax!eosp1!robison princeton!eosp1!robison (NOTE! NOT McMillan; Robison.)