This book discusses a famous problem that helped to define the field now known as topology: What is the minimum number of colors required to print a map so that no two adjoining countries have the same color? This problem remained unsolved until the 1950s, when it was finally cracked using a computer. This book discusses the history and mathematics of the problem, as well as the philosophical debate which ensued, regarding the validity of computer generated proofs.
It's History.- Topological maps.- Topological Version of The Four-Color Theorem.- From Topology to Combinatorics.- The Combinatorial Version of The Four-Color Theorem.- Reducibility.- The Quest for Unavoidable Sets.
Inhaltsverzeichnis
It's History.- Topological maps.- Topological Version of The Four-Color Theorem.- From Topology to Combinatorics.- The Combinatorial Version of The Four-Color Theorem.- Reducibility.- The Quest for Unavoidable Sets.
Klappentext
This book discusses a famous problem that helped to define the field now known as topology: What is the minimum number of colors required to print a map so that no two adjoining countries have the same color? This problem remained unsolved until the 1950s, when it was finally cracked using a computer. This book discusses the history and mathematics of the problem, as well as the philosophical debate which ensued, regarding the validity of computer generated proofs.
This elegant little book discusses the famous problem concerning the minimum number of colors required to print a map such that no two adjoining countries have the same color, no matter how convoluted the boundaries; this is one of the problems that came to define the field now known as topology. The book begins by discussing the history of the problem, and then goes into the mathematics, pleasantly enough that anyone with an elementary knowledge of geometry can follow it, but with enough rigor that a mathematician can also read it with pleasure.
