2008;
380 pp;
Softcover

MSC: Primary 00;

Print ISBN: 978-0-8218-4348-2

Product Code: MBK/53

List Price: $38.00

AMS Member Price: $30.40

MAA member Price: $34.20

**Electronic ISBN: 978-1-4704-2484-8
Product Code: MBK/53.E**

List Price: $38.00

AMS Member Price: $30.40

MAA member Price: $34.20

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#### Supplemental Materials

# Five-Minute Mathematics

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*Ehrhard Behrends*

Translated by David Kramer

How much math can you cover in five minutes?
Quite a bit, if you have a good guide. In this collection of one
hundred short essays, Ehrhard Behrends offers a tour through
contemporary and everyday mathematics. The topics range from pure
mathematics to applications of mathematics to observations about the
mathematics that surrounds us in daily life. Here, we read about the
parable of grains of rice on a chessboard, the mathematics of the
lottery, music and mathematics, intriguing paradoxes, the concept of
infinity, the Poincaré conjecture, quantum computers, and plenty
more.

Anyone who regularly reads the science section of a newspaper or
magazine will find much to enjoy in Five-Minute Mathematics.
Behrends makes very few assumptions about his readers, other than
general curiosity and some familiarity with high school mathematics.

The vignettes originally appeared in the author's newspaper column.
They have been extensively revised and expanded, and provided with
attractive illustrations and photographs.

#### Readership

Undergraduates, graduate students, and research mathematicians interested in general topics in mathematics; the mathematics of everyday life.

#### Reviews & Endorsements

This book, a breath of fresh air, makes mathematics a delight and fun for almost any reader. ... I highly recommend this book for any teacher looking for a way to get students interested in mathematics—again or for the first time.

-- Joyce Fischer, for NCTM's "Mathematics Teacher"

The book has remarkable breadth. It covers probability theory, number theory, the history of mathematics, finance, computer science, topology, music, famous numbers, and on and on. ... This book is sure to be enjoyed by everyone who loves mathematics. With chapters 3–5 pages long, it is the perfect book to read before bedtime, on the beach, or on the train or bus while commuting to work or school.

-- MAA Reviews

The columns have been carefully revised and extra material has been added when this seemed appropriate. The columns are a delight to read. They range very widely through mathematics. He has certainly raised public awareness with these fine columns, which are clearly and engagingly written, and he does not shy away from difficult topics whenhe can find a way to explain them at an appropriate level.

-- LMS Newsletter

One of the main achievements of this book, in the reviewer's opinion, is the fact that sophisticated mathematical ideas are presented in an accessible manner. The applications of mathematics are given much consideration, but the reader will also gain an appreciation for the beauty and power of the subject and the enjoyment that can be had from engaging with it. This book is aimed at the general reader and would be an excellent resource for mathematics teachers or anyone engaged in communicating mathematics to the general public.

-- Zentralblatt MATH

# Table of Contents

## Five-Minute Mathematics

- Cover Cover11 free
- Title page iii4 free
- Contents v6 free
- Foreword: “Five-minute mathematics” in 𝐷𝑖𝑒𝑊𝑒𝑙𝑡 xi12 free
- Translator’s note xv16 free
- Preface to the English edition xix20 free
- Preface to the German edition xxi22 free
- Acknowledgments xxiii24 free
- Introduction xxv26 free
- Chapter 1. You can’t beat the odds 130 free
- Chapter 2. Magical mathematics: The integers 534
- Chapter 3. How old is the captain? 837
- Chapter 4. Vertiginously large prime numbers 1140
- Chapter 5. Loss plus loss equals win 1443
- Chapter 6. When it comes to large numbers, intuition fails 1746
- Chapter 7. The key for encryption is the telephone book 2251
- Chapter 8. The village barber who shaves himself 2756
- Chapter 9. Quit while you’re ahead? 3160
- Chapter 10. Can a monkey create great literature? 3463
- Chapter 11. The birthday paradox 3766
- Chapter 12. Horror vacui 4271
- Chapter 13. Sufficient difficulties with the logic of mathematics are in fact a necessity 4574
- Chapter 14. To change or not to change? The Monty Hall problem 4877
- Chapter 15. In Hilbert’s Hotel there is always a vacancy 5887
- Chapter 16. That fascinating number pi 6190
- Chapter 17. How random events become calculable quantities 6493
- Chapter 18. A one-million-dollar prize: How are the prime numbers distributed? 6897
- Chapter 19. The five-dimensional cake 72101
- Chapter 20. One night stand 76105
- Chapter 21. Fly me to the Moon 80109
- Chapter 22. Using residues 83112
- Chapter 23. Top secret! 86115
- Chapter 24. Magical mathematics: Order amidst chaos 92121
- Chapter 25. How does one approach genius? 96125
- Chapter 26. On semitones and twelfth roots 101130
- Chapter 27. Why am I always standing in the wrong line? 105134
- Chapter 28. Zero: An undeservedly underrated number 109138
- Chapter 29. I love to count! 112141
- Chapter 30. Genius autodidact: The Indian mathematician Ramanujan 118147
- Chapter 31. I hate mathematics because... 121150
- Chapter 32. The traveling salesman: A modern odyssey 124153
- Chapter 33. Squaring the circle 127156
- Chapter 34. A step into the infinite 134163
- Chapter 35. Mathematics in your CD player 139168
- Chapter 36. The logarithm: A dying breed 142171
- Chapter 37. Prizeworthy mathematics 145174
- Chapter 38. Why axioms of all things? 148177
- Chapter 39. Proof by computer? 151180
- Chapter 40. The lottery: The small prizes 155184
- Chapter 41. Formulas = concentrated thought 158187
- Chapter 42. Endless growth 161190
- Chapter 43. How do quanta compute? 165194
- Chapter 44. Extremes! 169198
- Chapter 45. Infinitely small? 172201
- Chapter 46. Mathematical observations at the fire department 176205
- Chapter 47. The first mathematical proof is 2,500 years old 179208
- Chapter 48. There is transcendence in mathematics, though it has nothing to do with mysticism 183212
- Chapter 49. Is every even number the sum of two primes? 188217
- Chapter 50. Why we invert conditional probabilities incorrectly 192221
- Chapter 51. Millionaire or billionaire? 196225
- Chapter 52. Mathematics and chess 199228
- Chapter 53. “The book of nature is written in the language of mathematics” 202231
- Chapter 54. The search for Mersenne primes 206235
- Chapter 55. Berlin, eighteenth century: A beatuful formula is discovered 210239
- Chapter 56. The first really complicated number 213242
- Chapter 57. P = NP: In mathematics, is luck sometimes unnecessary? 216245
- Chapter 58. Happy 32nd birthday! 219248
- Chapter 59. Buffon’s needle 222251
- Chapter 60. Running hot and cold: Controlled cooling solves optimization problems 226255
- Chapter 61. Who didn’t pay? 230259
- Chapter 62. What can statistics tell us? 233262
- Chapter 63. Arbitrage 236265
- Chapter 64. Farewell to risk: Options 239268
- Chapter 65. Is mathematics a reflection of the world? 242271
- Chapter 66. Mathematics that you can hear 246275
- Chapter 67. Chance as composer 251280
- Chapter 68. Do dice have a guilty conscience? 255284
- Chapter 69. Strawberry ice cream can kill you! 258287
- Chapter 70. Prosperity for all 261290
- Chapter 71. No risk, thank you! 264293
- Chapter 72. A Nobel Prize in mathematics? 268297
- Chapter 73. Chance as reckoner: Monte Carlo methods 272301
- Chapter 74. Fuzzy logic 276305
- Chapter 75. Secret messages in the Bible? 279308
- Chapter 76. How knotted can a knot be? 283312
- Chapter 77. How much mathematics does a person need? 287316
- Chapter 78. Big, bigger, biggest 290319
- Chapter 79. It is probably correct 293322
- Chapter 80. Is the world a crooked place? 296325
- Chapter 81. Is there a mathematical bureau of standards? 299328
- Chapter 82. The butterfly that fluttered by 303332
- Chapter 83. Guaranteed to make you rich 307336
- Chapter 84. Don’t trust anyone over thirty 310339
- Chapter 85. Equality in mathematics 312341
- Chapter 86. Magical invariants 314343
- Chapter 87. Mathematics goes to the movies 318347
- Chapter 88. The lazy eight: Infinity 320349
- Chapter 89. Books need bigger margins! 323352
- Chapter 90. Visualizing internal organs with mathematics 327356
- Chapter 91. A brain in the computer 330359
- Chapter 92. Cogito, ergo sum 335364
- Chapter 93. Does the world have a hole? 339368
- Chapter 94. Complex numbers are not so complex as their name suggests 342371
- Chapter 95. M. C. Escher and infinity 347376
- Chapter 96. A one at the beginning is much more likely than a two 351380
- Chapter 97. The Leipzig town hall and the sunflower 354383
- Chapter 98. Information optimally packaged 360389
- Chapter 99. Four colors suffice! 364393
- Chapter 100. Mathematics makes billionaires 369398
- Further reading 373402
- Index 377406
- Back Cover Back Cover1410