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Huygens and Barrow, Newton and Hooke : pioneers in mathematical analysis and catastrophe theory from evolvents to quasicrystals

Author: V I Arnolʹd
Publisher: Basel ; Boston : Birkhaüser Verlag, 1990.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
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Genre/Form: History
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: V I Arnolʹd
ISBN: 0817623833 9780817623838 3764323833 9783764323837
OCLC Number: 21873606
Notes: Translation of: Gi︠u︡ĭgens i Barrou, Nʹi︠u︡ton i Guk.
Description: 118 pages : illustrations ; 21 cm
Contents: Huygens and Barrow, Newton and Hooke --
Ch. 1. The law of universal gravitation. 1. Newton and Hooke. 2. The problem of falling bodies. 3. The inverse square law. 4. The Principia. 5. Attraction of spheres. 6. Did Newton prove that orbits are elliptic? --
Ch. 2. Mathematical analysis. 7. Analysis by means of power series. 8. The Newton polygon. 9. Barrow. 10. Taylor series. 11. Leibniz. 12. Discussion on the invention of analysis --
Ch. 3. From evolvents to quasicrystals. 13. The evolvents of Huygens. 14. The wave fronts of Huygens. 15. Evolvents and the icosahedron. 16. The icosahedron and quasicrystals --
Ch. 4. Celestial mechanics. 17. Newton after the Principia. 18. The natural philosophy of Newton. 19. The triumphs of celestial mechanics. 20. Laplace's theorem on stability. 21. Will the Moon fall to Earth? 22. The three body problem. 23. The Titius-Bode law and the minor planets. 24. Gaps and resonances --
Ch. 5. Kepler's second law and the topology of Abelian integrals. 25. Newton's theorem on the transcendence of integrals. 26. Local and global algebraicity. 27. Newton's theorem on local non-algebraicity. 28. Analyticity of smooth algebraic curves. 29. Algebraicity of locally algebraically integrable ovals. 30. Algebraically non-integrable curves with singularities. 31. Newton's proof and modern mathematics --
Appendix 1. Proof that orbits are elliptic --
Appendix 2. Lemma XXVIII of Newton's Principia.
Other Titles: Gi︠u︡ĭgens i Barrou, Nʹi︠u︡ton i Guk.
Responsibility: V.I. Arnolʹd ; translated from the Russian by Eric J.F. Primrose.
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