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

## Rudolf Fritsch; Gerda Fritsch

Valutazione media 3,75
( su 4 valutazioni fornite da Goodreads )

This elegant little 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 such that no two adjoining countries have the same color, no matter how convoluted their boundaries. Many famous mathematicians have worked on the problem, but the proof eluded fomulation 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, both pleasantly enough that anyone with an elementary knowledge of geometry can follow it, and still with enough rigor that a mathematician can also read it with pleasure. 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?

Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.

From the Back Cover:

This elegant little book discusses a famous problem that helped to define the field now known as graph theory: what is the minimum number of colors required to print a map such that no two adjoining countries have the same color, no matter how convoluted their boundaries are. Many famous mathematicians have worked on the problem, but the proof eluded formulation until the 1970s, when it was finally cracked with a brute-force approach using a computer. The Four-Color Theorem begins by discussing the history of the problem up to the new approach given in the 1990s (by Neil Robertson, Daniel Sanders, Paul Seymour, and Robin Thomas). The book then goes into the mathematics, with a detailed discussion of how to convert the originally topological problem into a combinatorial one that is both elementary enough that anyone with a basic knowledge of geometry can follow it and also rigorous enough that a mathematician can read it with satisfaction. The authors discuss the mathematics and point to 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?

Fritsch of the University of Munich, Germany

Fritsch of the University of Munich, Germany

Fritsch of the University of Munich, Germany

Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.

Compra nuovo Guarda l'articolo
EUR 54,30

Spese di spedizione: EUR 2,57
In U.S.A.

Destinazione, tempi e costi

Aggiungere al carrello

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

Editore: Springer (1998)
ISBN 10: 0387984976 ISBN 13: 9780387984971
Nuovi Rilegato Quantità: 2
Da
Murray Media
(North Miami Beach, FL, U.S.A.)
Valutazione libreria

Descrizione libro Springer, 1998. Hardcover. Condizione libro: New. Codice libro della libreria P110387984976

Compra nuovo
EUR 54,30
Convertire valuta
Spese di spedizione: EUR 2,57
In U.S.A.
Destinazione, tempi e costi

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

Editore: Springer (1998)
ISBN 10: 0387984976 ISBN 13: 9780387984971
Nuovi Rilegato Quantità: 1
Da
Irish Booksellers
(Rumford, ME, U.S.A.)
Valutazione libreria

Descrizione libro Springer, 1998. Hardcover. Condizione libro: New. book. Codice libro della libreria 387984976

Compra nuovo
EUR 61,51
Convertire valuta
Spese di spedizione: GRATIS
In U.S.A.
Destinazione, tempi e costi

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

Editore: Springer (1998)
ISBN 10: 0387984976 ISBN 13: 9780387984971
Nuovi Rilegato Quantità: 1
Print on Demand
Da
Ergodebooks
(RICHMOND, TX, U.S.A.)
Valutazione libreria

Descrizione libro Springer, 1998. Hardcover. Condizione libro: New. 1. This item is printed on demand. Codice libro della libreria DADAX0387984976

Compra nuovo
EUR 60,58
Convertire valuta
Spese di spedizione: EUR 3,43
In U.S.A.
Destinazione, tempi e costi

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

Editore: Springer
ISBN 10: 0387984976 ISBN 13: 9780387984971
Nuovi Rilegato Quantità: 1
Da
Cloud 9 Books
(Wellington, FL, U.S.A.)
Valutazione libreria

Descrizione libro Springer. Hardcover. Condizione libro: New. 0387984976 New Condition. Codice libro della libreria NEW6.1126690

Compra nuovo
EUR 61,92
Convertire valuta
Spese di spedizione: EUR 4,29
In U.S.A.
Destinazione, tempi e costi

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

Editore: Springer (1998)
ISBN 10: 0387984976 ISBN 13: 9780387984971
Nuovi Rilegato Prima edizione Quantità: 1
Da
Irish Booksellers
(Rumford, ME, U.S.A.)
Valutazione libreria

Descrizione libro Springer, 1998. Hardcover. Condizione libro: New. book. Codice libro della libreria 0387984976

Compra nuovo
EUR 67,23
Convertire valuta
Spese di spedizione: GRATIS
In U.S.A.
Destinazione, tempi e costi

## 6.The Four-Color Theorem

Editore: Springer
ISBN 10: 0387984976 ISBN 13: 9780387984971
Nuovi Quantità: 1
Da
Majestic Books
(London, ,, Regno Unito)
Valutazione libreria

Descrizione libro Springer. Condizione libro: New. pp. xvi + 260. Codice libro della libreria 7551259

Compra nuovo
EUR 79,14
Convertire valuta
Spese di spedizione: EUR 6,15
Da: Regno Unito a: U.S.A.
Destinazione, tempi e costi