The Four-Color Theorem: History, Topological Foundations, and Idea of Proof

ISBN-13: 9780387984971 / Angielski / Twarda / 1998 / 260 str.

Rudolf Fritsch; R. Fritsch; G. Fritsch

Opis

This little book discusses a famous problem which helped to define the field now known as topology: what is the minimum number of colours required to print a map so that no two adjoining countries have the same colour, no matter how convoluted their boundaries? Many mathematicians have worked on the problem, but the proof eluded formulation until the 1950s, when it was finally cracked with a brute-force approach using a computer. The book begins by discussing the history of the problem, and then goes into the mathematics on such a level as to allow anyone with an elementary knowledge of geometry to follow it. It is equally designed with enough rigour to keep a mathematician occupied. The authors discuss the mathematics as well as the philosophical debate that ensued when the proof was announced: just what is a mathematical proof, if it takes a computer to provide one - and is such a thing a proof at all?