## Explorations in Mathematics |

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### Contents

The Fibonacci Sequence and its Variations | 22 |

Appendices | 42 |

Pythagorean Triplets | 48 |

Multiplication of Very Large Numbers | 65 |

Prime Numbers | 73 |

Perpetual Calendar and Biorhythms | 92 |

Construction of Tables of Logarithms | 111 |

Playing TicTacToe with the Computer | 126 |

Number Systems | 142 |

### Common terms and phrases

ANYTDEC2 Appendix 4.1 Aryabhata BASIC program bers biorhythm Brahmagupta calculate the value calendar coefficients column common logarithms consecutive terms converted correct decimal places decimal point decimal system deposit determine developed diagonal digits Diophantine equations Divide divisible END Appendix error Fibonacci sequence follows formula give given in Appendix Golden Rectangle GOSUB GOTO infinite number infinite series integer irrational number large numbers limiting number loop magic number magic square mathematical mathematicians method month multiplication Napierian natural numbers NEXTj nth term number of prime number of terms octal odd numbers player pocket calculator possible prime numbers primitive Pythagorean triplets PRINT Enter program in Appendix puzzle Pythagoras Pythagorean triplets quotient ratios of consecutive reader reciprocals REM Move number remainder rules Section seed-design selected shown in Figure solutions solve starting numbers Statements STEP Subroutine Tic-Tac-Toe tion twin primes variables variations white counters write