## The Penguin Dictionary of Curious and Interesting NumbersWhy was the number of Hardy's taxi significant? Why does Graham's number need its own notation? How many grains of sand would fill the universe? What is the connection between the Golden Ratio and sunflowers? Why is 999 more than a distress call? All these questions and a host more are answered in this fascinating book, which has now been newly revised, with nearly 200 extra entries and some 250 additions to the original entries. From minus one and its square root, via cyclic, weird, amicable, perfect, untouchable and lucky numbers, aliquot sequences, the Cattle problem, Pascal's triangle and the Syracuse algorithm, music, magic and maps, pancakes, polyhedra and palindromes, to numbers so large that they boggle the imagination, all you ever wanted to know about numbers is here. There is even a comprehensive index for those annoying occasions when you remember the name but can't recall the number. |

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### Contents

The Dictionary | |

Multiplyperfect numbers | 74 |

Mersenne numbers | 77 |

Amicable numbers | 94 |

Fermat numbers | 100 |

Sociable chains and aliquot sequences | 103 |

Kaprekar numbers | 105 |

The calendar | 108 |

Numerology | 113 |

The cattle problem | 177 |

Tables | 255 |

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### Common terms and phrases

2-digit 4-digit number 4th powers abundant number amicable numbers approximation arithmetical progression base binary calculated circle conjectured consecutive integers consecutive numbers counting cube cyclic permutation David Slowinski diagonals discovered distinct primes divided divisors dodecahedron equal equation Euler example Fermat numbers Fibonacci numbers Fibonacci sequence form 4n formula Golden Ratio Greeks hexagonal number icosahedron integers JRM v26 Kaprekar Kaprekar number large numbers largest number length Lucky numbers magic square mathematicians mathematics Mersenne number Mersenne prime multiple negative numbers notation number of digits number of primes Number Theory numbers less odd number palindromic prime pandigital Pascal Pascal's triangle pattern perfect number Plato Platonic solids prime factors prime number primorial problem proved Pythagorean triangle reciprocal repeated repunit Ribenboim right-angled triangle sequence of numbers Sloane Slowinski smallest number solution square root starts Subfactorial tetrahedral number theorem triangular numbers unit fractions values whole numbers zero