The Mathematical Coloring Book: Mathematics of Coloring and the Colorful Life of its CreatorsThis is a unique type of book; at least, I have never encountered a book of this kind. The best description of it I can give is that it is a mystery novel, developing on three levels, and imbued with both educational and philosophical/moral issues. If this summary description does not help understanding the particular character and allure of the book, possibly a more detailed explanation will be found useful. One of the primary goals of the author is to interest readers—in particular, young mathematiciansorpossiblypre-mathematicians—inthefascinatingworldofelegant and easily understandable problems, for which no particular mathematical kno- edge is necessary, but which are very far from being easily solved. In fact, the prototype of such problems is the following: If each point of the plane is to be given a color, how many colors do we need if every two points at unit distance are to receive distinct colors? More than half a century ago it was established that the least number of colors needed for such a coloring is either 4, or 5, or 6 or 7. Well, which is it? Despite efforts by a legion of very bright people—many of whom developed whole branches of mathematics and solved problems that seemed much harder—not a single advance towards the answer has been made. This mystery, and scores of other similarly simple questions, form one level of mysteries explored. In doing this, the author presents a whole lot of attractive results in an engaging way, and with increasing level of depth. |
Contents
3 | |
6 | |
The Problem 13 | 11 |
Polychromatic Number of the Plane and Results Near the Lower | 32 |
De BruijnErdos Reduction to Finite Sets and Results Near | 39 |
Continuum of 6Colorings of the Plane | 50 |
Chromatic Number of the Plane in Special Circumstances | 57 |
Coloring in Space | 67 |
How Does One Color Infinite Maps? A Bagatelle | 207 |
Paul Erdos | 227 |
De BruijnErdoss Theorem and Its History | 236 |
Ramsey and Folkman Numbers | 242 |
From Pigeonhole Principle to Ramsey Principle 263 | 262 |
Frank Plumpton Ramsey | 281 |
Ramsey Theory Before Ramsey and | 297 |
The Unsettling Years 19461951 | 449 |
Chromatic Number of a Graph | 79 |
Dimension of a Graph | 88 |
Embedding 4Chromatic Graphs in the Plane | 99 |
Embedding World Records | 110 |
Edge Chromatic Number of a Graph | 127 |
Carsten Thomassens 7Color Theorem | 140 |
How the FourColor Conjecture Was Born | 147 |
Victorian Comedy of Errors and Colorful Progress | 163 |
KempeHeawoods FiveColor Theorem and Taits Equivalence | 176 |
The FourColor Theorem | 187 |
The Great Debate | 195 |
Euclidean Ramsey Theory 485 | 484 |
Gallais Theorem | 505 |
Colored Integers in Service of Chromatic Number | 519 |
Application of BergelsonLeibmans and MordellFaltings | 525 |
Predicting the Future 533 | 532 |
Chromatic Number of the Plane | 553 |
Two Celebrated Problems | 567 |
595 | |
603 | |
Other editions - View all
The Mathematical Coloring Book: Mathematics of Coloring and the Colorful ... Alexander Soifer No preview available - 2014 |
The Mathematical Coloring Book: Mathematics of Coloring and the Colorful ... Alexander Soifer No preview available - 2008 |
Common terms and phrases
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