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 | |
Colored Plane | 11 |
De BruijnErdős 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 |
Chromatic Number of a Graph | 79 |
Dimension of a Graph | 88 |
From Pigeonhole Principle to Ramsey Principle 263 | 262 |
Frank Plumpton Ramsey | 281 |
Ramsey Theory Before Ramsey and | 297 |
Van der Waerden Tells the Story | 309 |
Whose Conjecture Did Van der Waerden Prove? Two Lives | 320 |
Life After Van | 347 |
The Early Years | 367 |
The Nazi Leipzig 19331945 | 393 |
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 |
How Does One Color Infinite Maps? A Bagatelle | 207 |
Paul Erdős | 227 |
De BruijnErdőss Theorem and Its History | 236 |
Ramsey and Folkman Numbers | 242 |
The Postwar Amsterdam 1945 | 418 |
The Unsettling Years 19461951 | 449 |
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
2-colored plane 4-chromatic 5-cycle adjacent Alexander Soifer Alexander Soifer 2009 algebra Amsterdam appointment Archive arithmetic progression Artin asked attached authors Axiom of Choice blue Brauer Brouwer Bruijn called Chapter chromatic number configurations conjecture construction contains a monochromatic Courant cut points cycle Dutch edges embedding Euclidean exists fact finite foundation vertices Gallai Geombinatorics George Szekeres German girth Göttingen Graham graph G Hadwiger Haken Heisenberg Henry Baudet infinite Issai Schur Jewish Kempe later Leipzig length letter lower bound Math Mathematical Coloring Book mathematicians mathematics monochrome unit Nazi Netherlands Open Problem paper Paul Erdős Paul Erdős's planar graph positive integer Princeton Prof Professor proof proved published Ramsey Theory Ramsey's result Richard Courant Richard Rado set theory Shelah solution student subgraph subset Szekeres Theorem Tool total chromatic unit distance graph University upper bound Utrecht Van der Waerden vertex Waerden write wrote Zürich