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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:   Book : EnglishView all editions and formats
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Genre/Form: History
Document Type: Book
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 p. : ill. ; 21 cm.
Contents: Huygens and Barrow, Newton and Hooke.- 1. The law of universal gravitation.- x 1. Newton and Hooke.- x 2. The problem of falling bodies.- x 3. The inverse square law.- x 4. The Principia.- x 5. Attraction of spheres.- x 6. Did Newton prove that orbits are elliptic?.- 2. Mathematical analysis.- x 7. Analysis by means of power series.- x 8. The Newton polygon.- x 9. Barrow.- x10. Taylor series.- x11. Leibniz.- x12. Discussion on the invention of analysis.- 3. From evolvents to quasicrystals.- x13. The evolvents of Huygens.- x14. The wave fronts of Huygens.- x15. Evolvents and the icosahedron.- x16. The icosahedron and quasicrystals.- 4. Celestial mechanics.- x17. Newton after the Principia.- x18. The natural philosophy of Newton.- x19. The triumphs of celestial mechanics.- x20. Laplace's theorem on stability.- x21. Will the Moon fall to Earth?.- x22. The three body problem.- x23. The Titius-Bode law and the minor planets.- x24. Gaps and resonances.- 5. Kepler's second law and the topology of Abelian integrals.- x25. Newton's theorem on the transcendence of integrals.- x26. Local and global algebraicity.- x27. Newton's theorem on local non-algebraicity.- x28. Analyticity of smooth algebraic curves.- x29. Algebraicity of locally algebraically integrable ovals.- x30. Algebraically non-integrable curves with singularities.- x31. Newton's proof and modern mathematics.- Appendix 1. Proof that orbits are elliptic.- Appendix 2. Lemma XXVIII of Newton's Principia.- Notes.
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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