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Exploring Continued Fractions: From the Integers to Solar Eclipses - Couverture souple

Simoson, Andrew J.

 
9781470461287: Exploring Continued Fractions: From the Integers to Solar Eclipses
Couverture souple
ISBN 10 : 1470461285 ISBN 13 : 9781470461287
Editeur : American Mathematical Society, 2019

Synopsis

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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

À propos de l'auteur

Andrew J. Simoson, King University, Bristol, TN

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
American Mathematical Society
Date d'édition
2019
Langue
anglais
ISBN 10 
1470461285
ISBN 13 
9781470461287
Reliure
Broché
Nombre de pages
480
Coordonnées du fabricant
non disponible
Personne responsable
non disponible