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June Barrow-Green

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

by June Barrow-Green (Author)

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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. <P>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. <P>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.

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"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

Product details

Publisher ‏ : ‎ American Mathematical Society (October 29, 1996)
Language ‏ : ‎ English
Paperback ‏ : ‎ 272 pages
ISBN-10 ‏ : ‎ 0821803670
ISBN-13 ‏ : ‎ 978-0821803677
Item Weight ‏ : ‎ 1.6 pounds
Dimensions ‏ : ‎ 7.5 x 0.75 x 10.5 inches

Best Sellers Rank: #2,017,112 in Books (See Top 100 in Books)
- #432 in Mathematics Reference (Books)
- #1,620 in Mathematics History
- #11,999 in Mathematics (Books)

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June Barrow-Green

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Neal J. King

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This book is somewhere between an historical essay and a blow-by-blow analysis of one of Poincare's most important papers, which gave rise to many significant developments in 20th-century mathematics. You have to really like the subject of differential equations to get into this.

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