## A Number for your Thoughts: Facts and Speculations About Numbers from Euclid to the Latest ComputersWhy do we count the way we do? What is a prime number or a friendly, perfect, or weird one? How many are there and who has found the largest yet known? What is the Baffling Law of Benford and can you really believe it? Do most numbers you meet in every day life really begin with a 1, 2, or 3? What is so special about 6174? Can cubes, as well as squares, be magic? What secrets lie hidden in decimals? How do we count the infinite, and is one infinity really larger than another? These and many other fascinating questions about the familiar 1, 2, and 3 are collected in this adventure into the world of numbers. Both entertaining and informative, A Number for Your Thoughts: Facts and Speculations about Numbers from Euclid to the Latest Computers contains a collection of the most interesting facts and speculations about numbers from the time of Euclid to the most recent computer research. Requiring little or no prior knowledge of mathematics, the book takes the reader from the origins of counting to number problems that have baffled the world's greatest experts for centuries, and from the simplest notions of elementary number properties all the way to counting the infinite. |

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### Contents

Counting | 1 |

The Search for Prime Numbers | 10 |

The World Record Holders | 19 |

The Distribution of Primes | 25 |

Prime Races Emirps and More | 33 |

The Baffling Law of Benford | 43 |

What is so Special about 6174? | 53 |

Number Patterns and Symmetries | 62 |

Magic Squares and Cubes | 117 |

How can Anything so Simple be so Difficult? | 124 |

Nearly All Numbers are Insane | 132 |

Cyclic Numbers and their Secret | 141 |

Pi a Transcendental Number | 152 |

Most Numbers are Normal but its Tough to Find One | 161 |

A Different Way of Counting Geometric Numbers | 169 |

Two Dimensional Numbers | 179 |

Numbers Perfect Friendly and Weird | 71 |

How do These Series End? | 86 |

Fermats Legendary Last Theorem | 94 |

Shapely Numbers and Mr Waring | 103 |

Counting the Infinite | 189 |

Update September 1985 | 200 |

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### Common terms and phrases

3-digit abundant numbers algebraic equations amicable pairs appear arithmetic number Benford big gee chapter complex numbers conjecture consecutive contain counting numbers cyclic number cycling decimal decimal places defined divisors emirps equal established Euler exactly divisible example exist fact Fermat primes Fermat's last theorem finite number follows fraction geometric numbers go on forever Goldbach Goldbach conjecture groups house number infinite infinity integers interest irrational numbers known large numbers largest logarithms magic constant magic cubes magic squares mathematical mathematicians means Mersenne prime multiplied number of digits number of primes number system odd numbers order-5 palindromic particular pattern perfect numbers polygons possible prime numbers prime twins problem proof random rational numbers real numbers rule sequence set of numbers simple smaller smallest number subtraction symbol Table transcendental numbers transfinite numbers triangular numbers true Waring's problem weird numbers write zero

### References to this book

GAMMA: Eulers Konstante, Primzahlstrände und die Riemannsche Vermutung Julian Havil Limited preview - 2007 |