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?
The Four-Color Theorem
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Text: English (translation)
Original Language: German
Original Language: German
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Four-Color Theorem, Four-Color Problem, Proof Let, Francis Guthrie, University College, Five-Color Theorem, Johns Hopkins University, United States, Augustus de Morgan, First Steps, George David, Harvard University, University of Illinois, American Journal of Mathematics, Heinrich Heesch, Arthur Bernhart, Basic Examples, Frederick Guthrie, Jean Mayer, John Koch, Paul Wernicke, Philip Franklin, Proof Suppose, Trinity College, William Whewell Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Four-Color Theorem, Four-Color Problem, Proof Let, Francis Guthrie, University College, Five-Color Theorem, Johns Hopkins University, United States, Augustus de Morgan, First Steps, George David, Harvard University, University of Illinois, American Journal of Mathematics, Heinrich Heesch, Arthur Bernhart, Basic Examples, Frederick Guthrie, Jean Mayer, John Koch, Paul Wernicke, Philip Franklin, Proof Suppose, Trinity College, William Whewell Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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This book cites 22
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- Four-colour Problem by Oystein Ore on page 30, Back Matter (1), and Back Matter (2)
- The Four-Color Problem: Assaults and Conquest by Thomas L. Saaty on page 184, and Back Matter
- Graph Theory (Cambridge Mathematical Library) by W. T. Tutte in Back Matter (1), and Back Matter (2)
- Differential Geometry of Curves and Surfaces by Manfredo Do Carmo in Back Matter
- Life of Sir William Rowan Hamilton (Volume 3) by R. Graves in Back Matter
See all 22 books this book cites
- Wittgenstein in America by Timothy McCarthy on page 103, and Back Matter
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