## 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. |

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### Contents

XCII | 301 |

XCIII | 304 |

XCIV | 307 |

XCV | 309 |

XCVII | 320 |

XCVIII | 321 |

XCIX | 330 |

C | 334 |

XV | 32 |

XVI | 39 |

XVII | 43 |

XVIII | 44 |

XIX | 47 |

XX | 50 |

XXI | 57 |

XXII | 60 |

XXIII | 65 |

XXIV | 67 |

XXV | 72 |

XXVI | 77 |

XXVII | 79 |

XXVIII | 82 |

XXIX | 86 |

XXX | 88 |

XXXI | 93 |

XXXII | 99 |

XXXIII | 101 |

XXXIV | 102 |

XXXV | 104 |

XXXVI | 106 |

XXXVII | 107 |

XXXVIII | 108 |

XXXIX | 110 |

XL | 111 |

XLI | 116 |

XLII | 117 |

XLIII | 121 |

XLIV | 124 |

XLV | 127 |

XLVI | 135 |

XLVII | 140 |

XLVIII | 145 |

XLIX | 147 |

L | 156 |

LI | 158 |

LII | 161 |

LIII | 163 |

LVII | 165 |

LVIII | 168 |

LIX | 173 |

LX | 176 |

LXI | 180 |

LXIII | 182 |

LXV | 185 |

LXVI | 187 |

LXVII | 195 |

LXVIII | 199 |

LXIX | 205 |

LXX | 207 |

LXXI | 209 |

LXXII | 211 |

LXXIII | 224 |

LXXIV | 227 |

LXXV | 228 |

LXXVI | 230 |

LXXVII | 236 |

LXXVIII | 239 |

LXXIX | 242 |

LXXX | 256 |

LXXXI | 261 |

LXXXII | 262 |

LXXXIII | 267 |

LXXXIV | 268 |

LXXXV | 272 |

LXXXVI | 277 |

LXXXVII | 280 |

LXXXVIII | 281 |

LXXXIX | 291 |

XC | 297 |

XCI | 299 |

CI | 336 |

CII | 340 |

CIII | 346 |

CIV | 347 |

CV | 348 |

CVI | 350 |

CVII | 353 |

CVIII | 356 |

CIX | 358 |

CX | 360 |

CXI | 366 |

CXII | 367 |

CXIII | 369 |

CXIV | 373 |

CXV | 377 |

CXVI | 380 |

CXVII | 383 |

CXVIII | 385 |

CXIX | 386 |

CXX | 387 |

CXXI | 392 |

CXXII | 393 |

CXXIII | 394 |

CXXIV | 406 |

CXXV | 416 |

CXXVI | 418 |

CXXVII | 421 |

CXXVIII | 427 |

CXXIX | 434 |

CXXX | 446 |

CXXXI | 449 |

CXXXII | 458 |

CXXXIII | 462 |

CXXXIV | 465 |

CXXXV | 472 |

CXXXVI | 474 |

CXXXVII | 480 |

CXXXVIII | 484 |

CXXXIX | 487 |

CXL | 500 |

CXLI | 505 |

CXLII | 509 |

CXLIV | 514 |

CXLV | 516 |

CXLVI | 517 |

CXLVII | 519 |

CL | 521 |

CLI | 525 |

CLII | 529 |

CLIII | 530 |

CLIV | 532 |

CLV | 535 |

CLVI | 537 |

CLVII | 540 |

CLVIII | 543 |

CLIX | 544 |

CLX | 546 |

CLXI | 550 |

CLXII | 553 |

CLXV | 554 |

CLXVI | 555 |

CLXVII | 557 |

CLXVIII | 560 |

CLXIX | 562 |

CLXX | 564 |

CLXXI | 567 |

569 | |

595 | |

603 | |

CLXXV | 606 |

### 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 Alexander Soifer Alexander Soifer 2009 algebra Amsterdam arithmetic progression Artin attached Axiom of Choice blue Brauer Brouwer Bruijn Chapter chromatic number combinatorial conﬁgurations conjecture construction contains a monochromatic Courant cut points cycle deﬁne deﬁnition difﬁcult Dutch e-mail edges Erd˝os’s Euclidean exists ﬁeld ﬁgures ﬁnd ﬁnding ﬁnite ﬁrst ﬁve foundation vertices G¨ottingen Geombinatorics geometry George Szekeres German girth Graham graph G Graph Theory Heisenberg Henry Baudet inﬁnite Issai Schur Kempe Kempe’s Leipzig letter lower bound Math Mathematical Coloring Book mathematicians mathematics Nazi Netherlands number theory O’Donnell Open Problem paper Paul Erd˝os planar graph positive integer Princeton Prof Professor proof prove published Ramsey numbers Ramsey Theory Ramsey’s result Richard Rado set theory Shelah solution student subgraph subset sufﬁcient Szekeres Theorem Tool total chromatic triangle unit distance graph University upper bound Utrecht Van der Waerden vertex Waerden wrote Z¨urich