Huygens and Barrow, Newton and Hooke: Pioneers in Mathematical Analysis and Catastrophe Theory from Evolvements to Quasicrystals (Paperback)

by Vladimir I. Arnol'd (Author) "The year 1987 was the 300th anniversary of the publication of Newton's Principia, the book that laid the foundations of the whole of modern theoretical..." (more)
Key Phrases: integrable oval, field whose strength, pentagonal symmetry, Royal Society, Johann Bernoulli (more...)

Editorial Reviews

Product Description
V.I. Arnold, who is renowned for his lively style, retraces the beginnings of mathematical analysis and theoretical physics in the works (and the intrigues!) of the great scientists of the 17th century. Some of Huygens' and Newton's ideas. several centuries ahead of their time, were developed only recently. The author follows the link between their inception and the breakthroughs in contemporary mathematics and physics. he book provides present-day generalizations of Newton's theorems on the elliptical shape of orbits and on the transcendence of abelian integrals; it offers a brief review of the theory of regular and chaotic movement in celestial mechanics, including the problem of ports in the distribution of smaller planets and a discussion of the structure of planetary rings.

Translated from the Russian by E.J.F. Primrose

Language Notes
Text: English (translation)
Original Language: Russian

Product Details

• Paperback: 120 pages
• Publisher: Birkhauser (September 1990)
• Language: English
• ISBN-10: 0817623833
• ISBN-13: 978-0817623838
• Product Dimensions: 8.3 x 5.8 x 0.4 inches
• Shipping Weight: 8.8 ounces
• Average Customer Review: 4.5 out of 5 stars See all reviews (2 customer reviews)
• Amazon.com Sales Rank: #1,975,738 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

6 of 7 people found the following review helpful:

5.0 out of 5 stars Arnol'd's view of history, February 4, 2004

By	Professor Joseph L. McCauley "Joseph L. McCauley" (Austria+Texas) - See all my reviews

Entertaining and opinionated survey of the history of the origins of mechanics, post-Galileo, Kepler and Descartes, by the greatest living theorist of classical mechanics. Arnol'd shows sympathy for Hooke and argues that Hooke, not Newton, should be given credit for the inverse square law of gravity. However, I find Newton's approach to be more convincing. Arnol'd praises Newton's geometric insight and reminds us that Leibnitz mechanized the rules of calculus so that (fortunately, I would say) it can be taught to idiots. Interesting and highly entertaining descriptions of the nonsense of the extreme formalization of simple mathematical problems (in the hands of the Bourbaki school of math, e.g.) can be found in the footnotes.

A note to students: classical mechanics, in most texts, is taught in totally unphysical postulational style, divorced from experiment/observation. This is an anachronism. If you ask the typical physics professor "What, exactly, is the origin of the inverse square law of gravity, how was it discovered?", then he/she will not be able to explain it. Textbooks, blindly present a postulatory exposition (bad physics!) and merely plug an assumed force law (where did it come from!?) into The Second Law and derive Kepler's orbits, but this is not an explanation how Newton arrived at "1/r^2" in the first place. Hooke's explanation can be found in the monograph reviewed here. Newton's original "inverse solution" can be found in my book "Classical Mechanics", where the connection of apples with the discovery of the law of gravity is also explained, following "Principia".

Having written all that, I strongly recommend this beautifully-written little monograph for both enlightenment and entertainment.

4.0 out of 5 stars Short and bubbly, January 14, 2006

By	Viktor Blasjo - See all my reviews (REAL NAME)

Chapter 1 is on the inverse square law of gravitation. The presentation is structured by the Newton-Hooke correspondence on experimental verification of the rotation of the earth, which provides impetus for the law while containing missteps that are fun to correct once the law is in place. Chapter 2 is a polemic account of the creation of the calculus if there ever was one: Newton understands everything better than anyone, while Leibniz is "clumsy" at best. Then Arnol'd loses his head in chapter 3: Huygens studied evolvents (involutes), but Arnol'd thinks that evolvents should be though of as discriminants of groups generated by reflections, so the study of quasicrystals is really "the completion of the research begun be Huygens". Chapter 4 is a hodgepodge of celestial mechanics fun-facts. Arnol'd is his usual provocative self again in chapter 5, arguing that the Principia contains "an astonishingly modern topological proof of a remarkable theorem on the transcendence of abelian integrals".