Poincare and the Three Body Problem (History of Mathematics, V. 11) (History of Mathematics, 11) - Softcover

June Barrow-Green

Softcover

ISBN 10: 0821803670 ISBN 13: 9780821803677

Publisher: American Mathematical Society, 1996

Synopsis

The idea of chaos figures prominently in mathematics today. It arose in the work of one of the greatest mathematicians of the late 19th century, Henri Poincaré, on a problem in celestial mechanics: the three body problem. This ancient problem--to describe the paths of three bodies in mutual gravitational interaction--is one of those which is simple to pose but impossible to solve precisely.

Poincaré's famous memoir on the three body problem arose from his entry in the competition celebrating the 60th birthday of King Oscar of Sweden and Norway. His essay won the prize and was set up in print as a paper in Acta Mathematica when it was found to contain a deep and critical error. In correcting this error Poincaré discovered mathematical chaos, as is now clear from Barrow-Green's pioneering study of a copy of the original memoir annotated by Poincaré himself, recently discovered in the Institut Mittag-Leffler in Stockholm.

Poincaré and the Three Body Problem opens with a discussion of the development of the three body problem itself and Poincaré's related earlier work. The book also contains intriguing insights into the contemporary European mathematical community revealed by the workings of the competition. After an account of the discovery of the error and a detailed comparative study of both the original memoir and its rewritten version, the book concludes with an account of the final memoir's reception, influence and impact, and an examination of Poincaré's subsequent highly influential work in celestial mechanics.

About this title

Review

"Delightful and interesting to read ... will help professors ... provide some very interesting (and needed) historical background to their lectures. Any serious student of mathematical history will enjoy this treatise." ---- Applied Mechanics Reviews

"This is a superb piece of work and it throws new light on one of the most fundamental topics of mechanics ... This book can be thoroughly recommended." ---- Mathematical Reviews

"A fair treatment and a nice description of the history regarding Poincaré and the three body problem ... of interest to many mathematicians, physicists and astronomers ... a balanced and very readable book ... recommend[ed] ... to all mathematically trained people with an interest in the historical origins of chaos." ---- Nonlinear Science Today

Edition details

• Publisher: American Mathematical Society
• Publication date: 1996
• ISBN 10: 0821803670
• ISBN 13: 9780821803677
• Binding: Paperback
• Language: English
• Number of pages: 272