Exploring Continued Fractions: From the Integers to Solar Eclipses (Dolciani Mathematical Expositions, 53) - Softcover

Simoson, Andrew J.

 
9781470461287: Exploring Continued Fractions: From the Integers to Solar Eclipses (Dolciani Mathematical Expositions, 53)
Softcover
ISBN 10: 1470461285 ISBN 13: 9781470461287
Verlag: American Mathematical Society, 2021

Inhaltsangabe

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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Über die Autorin bzw. den Autor

Andrew J. Simoson, King University, Bristol, TN

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Verlag
American Mathematical Society
Erscheinungsdatum
2021
Sprache
Englisch
ISBN 10 
1470461285
ISBN 13 
9781470461287
Einband
Taschenbuch
Anzahl der Seiten
480
Kontakt zum Hersteller
Nicht verfügbar
Verantwortliche Person
preigu
mail@preigu.de

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Osnabrück
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Deutschland

Weitere beliebte Ausgaben desselben Titels

9781470447953: Exploring Continued Fractions: From the Integers to Solar Eclipses (Dolciani Mathematical Expositions, Band 53)

Vorgestellte Ausgabe

ISBN 10:  1470447959 ISBN 13:  9781470447953
Verlag: American Mathematical Society, 2019
Hardcover