Four Colors Suffice (eBook)

How the Map Problem Was Solved - Revised Color Edition

Robin Wilson (Autor)

eBook Download: PDF

2021
224 Seiten
Princeton University Press (Verlag)
978-0-691-23756-5 (ISBN)

Infos

On October 23, 1852, Professor Augustus De Morgan wrote a letter to a colleague, unaware that he was launching one of the most famous mathematical conundrums in history--one that would confound thousands of puzzlers for more than a century. This is the amazing story of how the "e;map problem"e; was solved. The problem posed in the letter came from a former student: What is the least possible number of colors needed to fill in any map (real or invented) so that neighboring counties are always colored differently? This deceptively simple question was of minimal interest to cartographers, who saw little need to limit how many colors they used. But the problem set off a frenzy among professional mathematicians and amateur problem solvers, among them Lewis Carroll, an astronomer, a botanist, an obsessive golfer, the Bishop of London, a man who set his watch only once a year, a California traffic cop, and a bridegroom who spent his honeymoon coloring maps. In their pursuit of the solution, mathematicians painted maps on doughnuts and horseshoes and played with patterned soccer balls and the great rhombicuboctahedron. It would be more than one hundred years (and countless colored maps) later before the result was finally established. Even then, difficult questions remained, and the intricate solution--which involved no fewer than 1,200 hours of computer time--was greeted with as much dismay as enthusiasm. Providing a clear and elegant explanation of the problem and the proof, Robin Wilson tells how a seemingly innocuous question baffled great minds and stimulated exciting mathematics with far-flung applications. This is the entertaining story of those who failed to prove, and those who ultimately did prove, that four colors do indeed suffice to color any map. This new edition features many color illustrations. It also includes a new foreword by Ian Stewart on the importance of the map problem and how it was solved.

Produkt-Details

• Erscheint lt. Verlag: 12.10.2021
• Reihe/Serie: Princeton Science Library
• Reihe/Serie: Princeton Science Library
• Vorwort: Ian Stewart
• Zusatzinfo: 87 color illus. 18 halftones. 60 line illus. 2 maps.
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geschichte der Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Mathematische Spiele und Unterhaltung
• Themenwelt: Naturwissenschaften ► Geowissenschaften ► Geografie / Kartografie
• Schlagworte: Acta Mathematica • Alfred Kempe • Alice Liddell • A Mathematician's Apology • American Mathematical Society • analytical engine • Andrew Wiles • Arthur Cayley • Augustus De Morgan • Bertrand Russell • Buckminster Fuller • Calculation • Charles Babbage • Charles Sanders Peirce • Chauncey Wright • chromatic polynomial • Claude Berge • coefficient • Common Struggle • Concepts of Modern Mathematics • conjecture • counterexample • Counting • Daniel Gorenstein • David Hilbert • decimal • De Morgan's Laws • diagram • Diagram (category theory) • Digon • Discharging method (discrete mathematics) • Divisibility rule • dodecahedron • equilateral triangle • Euler's formula • Felix Klein • Fellow of the Royal Society • Fermat's Last Theorem • FORTRAN • Four Color • Four Color Theorem • Fourth power • Geometry • George David Birkhoff • Gerhard Ringel • G. H. Hardy • Gödel's Incompleteness Theorems • graph coloring • graph theory • Great Disappointment • Grigori Perelman • G. Spencer-Brown • Hamiltonian path • Harvard University • Hassler Whitney • Heawood conjecture • Heinrich Heesch • Henri Lebesgue • Hermann Weyl • icosahedron • icosian calculus • Icosian Game • James Joseph Sylvester • Journal of Combinatorial Theory • Kartar Singh Sarabha • Kenneth Appel • Laws of Form • Lecture • Leipzig • Leonhard Euler • Lewis Carroll • Lipman Bers • London Mathematical Society • map coloring • Mathematical folklore • Mathematical Induction • Mathematical problem • Mathematical Proof • mathematician • Mathematics • Natural number • New Scientist • Number Theory • octahedron • Oswald Veblen • Philip Franklin • polyhedron • polynomial • Popular Mathematics • Prime number • Principia Mathematica • Proceedings • Pure Mathematics • Quadratic equation • regular polyhedron • result • Richard Courant • Ring size • Robin Wilson (mathematician) • Root of unity • Rule Of Thumb • Scientific American • Semiregular polyhedron • Significant figures • Sign (mathematics) • Simon Newcomb • Simon Singh • Simple group • skepticism • Strategic Communication • Supercomputer • Tait's conjecture • Technische Hochschule • Tensor • tetrahedron • The New York Times • Theorem • Thesis • Thomas Kirkman • Thought experiment • To this Day • Uncertainty • University of Bristol • University of Kiel • University of Zurich • Variable (mathematics) • Walter Feit • Wiles's proof of Fermat's Last Theorem • William Rowan Hamilton • Wolfgang Haken • W. T. Tutte • W. W. Rouse Ball • Yale University
• ISBN-10: 0-691-23756-5 / 0691237565
• ISBN-13: 978-0-691-23756-5 / 9780691237565