## Dead Reckoning: Calculating Without InstrumentsThis volume describes techniques of computation and approximation that may be used to mentally and rapidly calculate mathematical quantities, including results of arithmetic operations and values of elementary functions. These methods range from very old to recent to brand new. They are not shortcuts, rather, the book is aimed at sharpening the mental skills needed to perform mathematical acrobatics. |

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### Contents

A Time for Reckoning | 7 |

Roots | 77 |

Logarithms and Their Inverses | 113 |

Copyright | |

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### Common terms and phrases

A. C. Aitken accurate actual value addition Aitken American Mathematical Monthly an+1 an+i an+l angle arccos arctan arrive casting out nines common logarithms consider continued fraction convenient cube root decimal places decimal point denominator derive divide divisibility tests earlier elevens test eliminated Equation 22 Error curve approximation estimate Euclid's Algorithm example f(an Fermat's method find log form 4k formula given number giving greatest common divisor Halley's method integer inverse large number last digit less lightning calculators logarithms Mathematics Magazine melded memorized mental calculation mod 9 modular arithmetic mult multidigit number multiple Newton-Raphson method nines test number ending number of digits obtained original number perform possible values prime factors prime number principal convergents provides quotient range rational approximations recurring group remainder repeating group result sieve simplify single-digit square root step subtract Table techniques term three-digit tions triangular numbers trigonometric truncating two-digit endings two-digit numbers units digit