The Mathematical Coloring Book: Mathematics of Coloring and the Colorful Life of its Creators

Front Cover
Springer Science & Business Media, Oct 13, 2008 - Mathematics - 607 pages
This 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

VII
3
X
4
XI
6
XII
7
XIII
8
XIV
10
XV
11
XVII
21
CXVIII
301
CXX
304
CXXI
307
CXXII
309
CXXIV
320
CXXVII
321
CXXVIII
330
CXXIX
334

XX
32
XXI
39
XXII
43
XXVI
44
XXVII
47
XXVIII
50
XXIX
57
XXX
60
XXXII
65
XXXIII
67
XXXIV
72
XXXV
77
XXXVI
79
XXXVIII
82
XXXIX
86
XL
88
XLI
93
XLII
99
XLIV
101
XLV
102
XLVII
104
XLIX
106
L
107
LI
108
LII
110
LIII
111
LIV
116
LV
117
LVI
121
LVII
124
LVIII
127
LX
135
LXI
140
LXII
145
LXIII
147
LXV
156
LXVI
158
LXVII
161
LXVIII
163
LXIX
165
LXX
168
LXXI
173
LXXII
176
LXXIV
180
LXXVI
182
LXXVIII
185
LXXIX
187
LXXXI
195
LXXXIII
199
LXXXIV
205
LXXXV
207
LXXXVI
209
LXXXIX
211
XC
224
XCI
227
XCII
228
XCIII
230
XCIV
236
XCVI
239
XCVII
242
CI
256
CII
261
CIII
262
CIV
267
CV
268
CVII
272
CVIII
277
CIX
280
CX
281
CXII
291
CXIII
297
CXV
299
CXXX
336
CXXXI
340
CXXXII
346
CXXXIII
347
CXXXV
348
CXXXVI
350
CXXXVII
353
CXXXVIII
356
CXXXIX
358
CXL
360
CXLI
366
CXLII
367
CXLIV
369
CXLV
373
CXLVI
377
CXLVII
380
CXLVIII
383
CXLIX
385
CL
386
CLI
387
CLII
392
CLIII
393
CLVI
394
CLVII
406
CLVIII
416
CLIX
418
CLXII
421
CLXIII
427
CLXIV
434
CLXV
446
CLXVI
449
CLXVIII
458
CLXIX
462
CLXX
465
CLXXI
472
CLXXII
474
CLXXIII
480
CLXXIV
484
CLXXVII
487
CLXXIX
500
CLXXXII
505
CLXXXIII
509
CLXXXV
514
CLXXXVI
516
CLXXXVII
517
CLXXXVIII
519
CLXXXIX
521
CXCI
525
CXCII
529
CXCIII
530
CXCIV
532
CXCV
535
CXCVII
537
CXCVIII
540
CXCIX
543
CC
544
CCI
546
CCII
550
CCIII
553
CCV
554
CCVI
555
CCVII
557
CCX
560
CCXI
562
CCXII
564
CCXIII
567
CCXV
569
CCXVI
595
CCXVII
603
CCXVIII
606
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About the author (2008)

Alexander Soifer is a Russian born and educated American mathematician, a professor of mathematics at the University of Colorado, an author of some 200 articles on mathematics, history of mathematics, mathematics education, film reviews, etc. He is Senior Vice President of the World Federation of National Mathematics Competitions, which in 2006 awarded him The Paul Erdös Award. 26 years ago Soifer founded has since chaired The Colorado Mathematical Olympiad, and served on both USSR and USA Mathematical Olympiads committees. Soifer’s Erdös number is 1.

Springer has contracted his 7 books. "The Mathematical Coloring Book" is coming out in October 2008; 4 books will appear in 2009; followed by "Life and Fate: In Search of Van der Waerden", and a joint book with the late Paul Erdos “Problems of p.g.o.m. Erdos."

The author's previous books were self-published and received many positive reviews, below are excerpts from reviews of "How Does One Cut A Triangle?:

"Why am I urging you to read this? Mainly because it is such a refreshing book. Professor Soifer makes the problems fascinating, the methods of attack even more fascinating, and the whole thing is enlivened by anecdotes about the history of the problems, some of their recent solvers, and the very human reactions of the author to some beautiful mathematics. Most of all, the book has charm, somehow enhanced by his slightly eccentric English, sufficient to carry the reader forward without minding being asked to do rather a lot of work.

I am tempted to include several typical quotations but I'll restrain myself to two: From Chapter 8 "Here is an easy problem for your entertainment. Problem 8.1.2. Prove that for any parallelogram P, S(P)=5. Now we have a new problem, therefore we are alive! And the problem is this: what are all possible values of our newly introduced function S(F)? Can the function S(F) help us to classify geometry figures?"

And from an introduction by Cecil Rousseau:

‘There is a view, held by many, that mathematics books are dull. This view is not without support. It is reinforced by numerous examples at all levels, from elementary texts with page after page of mind-numbing drill to advanced books written in a relentless Theorem-Proof style. "How does one cut a triangle?" is an entirely different matter. It reads like an adventure story. In fact, it is an adventure story, complete with interesting characters, moments of exhilaration, examples of serendipity, and unanswered questions. It conveys the spirit of mathematical discovery and it celebrates the event as have mathematicians throughout history.’

And this isn't just publishers going over the top - it's all true!"

-- JOHN Baylis in The Mathematical Gazette

Soifer's work can rightly be called a "mathematical gem."


-- JAMES N. BOYD in Mathematics Teacher

This delightful book considers and solves many problems in dividing triangles into n congruent pieces and also into similar pieces, as well as many extremal problems about placing points in convex figures. The book is primarily meant for clever high school students and college students interested in geometry, but even mature mathematicians will find a lot of new material in it. I very warmly recommend the book and hope the readers will have pleasure in thinking about the unsolved problems and will find new ones.


-- PAUL ERDÖS



It is impossible to convey the spirit of the book by merely listing the problems considered or even a number of solutions. The manner of presentation and the gentle guidance toward a solution and hence to generalizations and new problems takes this elementary treatise out of the prosaic and into the stimulating realm of mathematical creativity. Not only young talented people but dedicated secondary teachers and even a few mathematical sophisticates will find this reading both pleasant and profitable.


-- L. M. KELLY in Mathematical Reviews

We do not often have possibilities to look into a creative workshop of a mathematician... The beginner, who is interested in the book, not only comprehends a situation in a creative mathematical studio, not only is exposed to good mathematical taste, but also acquires elements of modern mathematical culture. And (not less important) the reader imagines the role and place of intuition and analogy in mathematical investigation; he or she fancies the meaning of generalization in modern mathematics and surprising connections between different parts of this science (that are, as one might think, far from each other) that unite them... This makes the book alive, fresh, and easily readable. Alexander Soifer has produced a good gift for the young lover of mathematics. And not only for youngsters; the book should be interesting even to professional mathematicians.


V. G. BOLTYANSKI in SIAM Review


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