## Five-minute MathematicsThis collection of one hundred short essays gives readers a grand tour through contemporary and everyday mathematics. Behrends provides classics from his newspaper column in Die Welt, expands and illustrates them, and gives readers just enough information at a time to build mastery of concepts and applications. The topics range from pure mathematics to applied math, but all essays are suspenseful and fun to read. This is a very handy tool for teachers of all levels of mathematics (even elementary school children will be able to handle some of the topics), and Behrends assumes his readership has and interest but only a minimal background in mathematics so the essays are accessible but not dumbed-down. |

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### Contents

You Cant Beat the Odds | 1 |

Magical Mathematics The Integers | 5 |

How Old Is the Captain? | 8 |

Vertiginously Large Prime Numbers | 11 |

Loss Plus Loss Equals Win | 14 |

When It Comes to Large Numbers Intuition Fails | 17 |

The Key for Encryption Is in the Telephone Book | 22 |

The Village Barber Who Shaves Himself | 27 |

The Book of Nature Is Written in the Language of Mathematics | 202 |

The Search for Mersenne Primes | 206 |

Berlin Eighteenth Century A Beautiful Formula Is Discovered | 210 |

The First Really Complicated Number | 213 |

P NP In Mathematics Is Luck Sometimes Unnecessary? | 216 |

Happy 32nd Birthday | 219 |

Buffons Needle | 222 |

Running Hot and Cold Controlled Cooling Solves Optimization Problems | 226 |

Quit While Youre Ahead? | 31 |

Can a Monkey Create Great Literature? | 34 |

The Birthday Paradox | 37 |

Horror Vacui | 42 |

Sufficient Difficulties with the Logic of Mathematics Are in Fact a Necessity | 45 |

To Change or Not to Change? The Monty Hall Problem | 48 |

In Hilberts Hotel There Is Always a Vacancy | 58 |

That Fascinating Number Pi | 61 |

How Random Events Become Calculable Quantities | 64 |

A OneMillionDollar Prize How Are the Prime Numbers Distributed? | 68 |

The FiveDimensional Cake | 72 |

One Night Stand | 76 |

Fly Me to the Moon | 80 |

Using Residues | 83 |

Top Secret | 86 |

Magical Mathematics Order amidst Chaos | 92 |

How Does One Approach Genius? | 96 |

On Semitones and Twelfth Roots | 101 |

Why Am I Always Standing in the Wrong Line? | 105 |

Zero An Undeservedly Underrated Number | 109 |

I Love to Count | 112 |

Genius Autodidact The Indian Mathematician Ramanujan | 118 |

I Hate Mathematics Because | 121 |

The Traveling Salesman A Modern Odyssey | 124 |

Squaring the Circle | 127 |

A Step into the Infinite | 134 |

Mathematics in Your CD Player | 139 |

The Logarithm A Dying Breed | 142 |

Prizeworthy Mathematics | 145 |

Why Axioms of All Things? | 148 |

Proof by Computer? | 151 |

The Lottery The Small Prizes | 155 |

Formulas Concentrated Thought | 158 |

Endless Growth | 161 |

How Do Quanta Compute? | 165 |

Extremes | 169 |

Infinitely Small? | 172 |

Mathematical Observations at the Fire Department | 176 |

The First Mathematical Proof Is 2500 Years Old | 179 |

There Is Transcendence in Mathematics Though It Has Nothing to Do with Mysticism | 183 |

Is Every Even Number the Sum of Two Primes? | 188 |

Why We Invert Conditional Probabilities Incorrectly | 192 |

Millionaire or Billionaire? | 196 |

Mathematics and Chess | 199 |

Who Didnt Pay? | 230 |

What Can Statistics Tell Us? | 233 |

Arbitrage | 236 |

Farewell to Risk Options | 239 |

Is Mathematics a Reflection of the World? | 242 |

Mathematics That You Can Hear | 246 |

Chance as Composer | 251 |

Do Dice Have a Guilty Conscience? | 255 |

Strawberry Ice Cream Can Kill You | 258 |

Prosperity for All | 261 |

No Risk Thank You | 264 |

A Nobel Prize in Mathematics? | 268 |

Chance as Reckoner Monte Carlo Methods | 272 |

Fuzzy Logic | 276 |

Secret Messages in the Bible? | 279 |

How Knotted Can a Knot Be? | 283 |

How Much Mathematics Does a Person Need? | 287 |

Big Bigger Biggest | 290 |

It Is Probably Correct | 293 |

Is the World a Crooked Place? | 296 |

Is There a Mathematical Bureau of Standards? | 299 |

The Butterfly That Fluttered By | 303 |

Guaranteed to Make You Rich | 307 |

Dont Trust Anyone over Thirty | 310 |

Equality in Mathematics | 312 |

Magical Invariants | 314 |

Mathematics Goes to the Movies | 318 |

The Lazy Eight Infinity | 320 |

Books Need Bigger Margins | 323 |

Visualizing Internal Organs with Mathematics | 327 |

A Brain in the Computer | 330 |

Cogito Ergo Sum | 335 |

Does the World Have a Hole? | 339 |

Complex Numbers Are Not So Complex as Their Name Suggests | 342 |

M C Escher and Infinity | 347 |

A One at the Beginning Is Much More Likely Than a Two | 351 |

The Leipzig Town Hall and the Sunflower | 354 |

Information Optimally Packaged | 360 |

Four Colors Suffice | 364 |

Mathematics Makes Billionaires | 369 |

Further Reading | 373 |

377 | |

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