Andrew J. Simoson's Books

Exploring Continued Fractions: From the Integers to Solar Eclipses

By: Andrew J. Simoson

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Exploring Continued Fractions: From the Integers to Solar Eclipses

By: Andrew J. Simoson

There is a nineteen-year recurrence in the apparent position of the sun and moon against the background of the stars, a pattern observed long ago by the Babylonians. In the course of those nineteen years the Earth experiences 235 lunar cycles. Suppose we calculate the ratio of Earth's period about the sun to the moon's period about Earth. That ratio has 235/19 as one of its early continued fraction convergents, which explains the apparent periodicity. Exploring Continued Fractions explains this and other recurrent phenomena—astronomical transits and conjunctions, lifecycles of cicadas, eclipses—by way of continued fraction expansions. The deeper purpose is to find patterns, solve puzzles, and discover some appealing number theory. The reader will explore several algorithms for computing continued fractions, including some new to the literature. He or she will also explore the surprisingly large portion of number theory connected to continued fractions: Pythagorean triples, Diophantine equations, the Stern-Brocot tree, and a number of combinatorial sequences. The book features a pleasantly discursive style with excursions into music (The Well-Tempered Clavier), history (the Ishango bone and Plimpton 322), classics (the shape of More's Utopia) and whimsy (dropping a black hole on Earth's surface). Andy Simoson has won both the Chauvenet Prize and Pólya Award for expository writing from the MAA and his Voltaire's Riddle was a Choice magazine Outstanding Academic Title. This book is an enjoyable ramble through some beautiful mathematics. For most of the journey the only necessary prerequisites are a minimal familiarity with mathematical reasoning and a sense of fun.

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Page Count

480

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470461285

ISBN 13

9781470461287

Hesiod's Anvil

Falling and Spinning through Heaven and Earth

By: Andrew J. Simoson

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Hesiod's Anvil

Falling and Spinning through Heaven and Earth

By: Andrew J. Simoson

This book is about models of motion as enunciated by poets, philosophers, storytellers, and early scientists. By using popular literature and philosophy to bring the mechanics of motion alive, blending with equal voice both romantic whimsy and derived equations.

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Page Count

362

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470457253

ISBN 13

9781470457259

Hesiod's Anvil

Falling and Spinning Through Heaven and Earth

By: Andrew J. Simoson

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Hesiod's Anvil

Falling and Spinning Through Heaven and Earth

By: Andrew J. Simoson

This book is about how poets, philosophers, storytellers, and scientists have described motion, beginning with Hesiod, who imagined that the expanse of heaven and the depth of hell was the distance that an anvil falls in nine days. The reader will learn that Dante's implicit model of the earth implies a black hole at its core, that Edmond Halley championed a hollow earth, and that Da Vinci knew that the acceleration due to Earth's gravity was a constant. There are chapters modeling Jules Verne's and H.G. Wells' imaginative flights to the moon and back, analyses of Edgar Alan Poe's descending pendulum, and the solution to an old problem perhaps inspired by one of the seven wonders of the ancient world. It blends with equal voice romantic whimsy and derived equations, and anyone interested in mathematics will find new and surprising ideas about motion and the people who thought about it.

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Page Count

368

Publisher

MAA

Published Date

ISBN 10

0883853361

ISBN 13

9780883853368

Exploring Continued Fractions: From the Integers to Solar Eclipses

By: Andrew J. Simoson

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Exploring Continued Fractions: From the Integers to Solar Eclipses

By: Andrew J. Simoson

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Age

Page Count

503

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470447959

ISBN 13

9781470447953

Book's by Andrew J. Simoson

Exploring Continued Fractions: From the Integers to Solar Eclipses

Exploring Continued Fractions: From the Integers to Solar Eclipses

Hesiod's Anvil

Hesiod's Anvil

Hesiod's Anvil

Hesiod's Anvil

Exploring Continued Fractions: From the Integers to Solar Eclipses

Exploring Continued Fractions: From the Integers to Solar Eclipses

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