## Mathematics: The Science of Patterns: The Search for Order in Life, Mind and the UniverseTo most people, mathematics means working with numbers. But as Keith Devlin shows in Mathematics: The Science of Patterns, this definition has been out of date for nearly 2,500 years. Mathematicians now see their work as the study of patterns—real or imagined, visual or mental, arising from the natural world or from within the human mind.Using this basic definition as his central theme, Devlin explores the patterns of counting, measuring, reasoning, motion, shape, position, and prediction, revealing the powerful influence mathematics has over our perception of reality. Interweaving historical highlights and current developments, and using a minimum of formulas, Devlin celebrates the precision, purity, and elegance of mathematics. |

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### Contents

Reasoning and Communicating 3 7 | 37 |

Motion and Change | 73 |

Shape | 105 |

Symmetry and Regularity | 145 |

Position | 173 |

Postscript | 209 |

### Common terms and phrases

addition algebraic angle sum arithmetic axioms Boole's calculus capture century circle complex numbers conjecture cube curve denote describe differential dimensions edges ematics equation Euclid's Euclidean geometry Euler Euler characteristic example face fact Fermat's last theorem Fermat's little theorem figure finite formula function Gauss given gradient Greek hexagonal hypersphere idea illustrated infinite series integers kind knot known lattice Leibniz logic look loop M. C. Escher mathe mathematicians mathematics maticians matics means method Mobius band Mordell conjecture natural numbers notation notion number theory objects packing particular plane polynomial possible postulate predicate predicate logic prime number problem projective geometry proof properties proposition propositional logic proved Pythagorean real numbers regular solids result set theory solution solve space sphere sphere packing square straight line surface syllogism symmetry group terns three-dimensional tiling tion topological transformations triangle true two-dimensional vector