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Mathematical Understanding of Nature: Essays on Amazing Physical Phenomena and Their Understanding by Mathematicians

About this Title

V. I. Arnold. Translated by Alexei Sossinsky and Olga Sipacheva

Publication: AMS Non-Series Monographs
Publication Year: 2014; Volume 85
ISBNs: 978-1-4704-1701-7 (print); 978-1-4704-1889-2 (online)
DOI: https://doi.org/10.1090/mbk/085

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Table of Contents

Front/Back Matter

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Chapters

• Chapter 1. The eccentricity of the Keplerian orbit of Mars
• Chapter 2. Rescuing the empennage
• Chapter 3. Return along a sinusoid
• Chapter 4. The Dirichlet integral and the Laplace operator
• Chapter 5. Snell’s law of refraction
• Chapter 6. Water depth and Cartesian science
• Chapter 7. A drop of water refracting light
• Chapter 8. Maximal deviation angle of a beam
• Chapter 9. The rainbow
• Chapter 10. Mirages
• Chapter 11. Tide, Gibbs phenomenon, and tomography
• Chapter 12. Rotation of a liquid
• Chapter 13. What force drives a bicycle forward?
• Chapter 14. Hooke and Keplerian ellipses and their conformal transformations
• Chapter 15. The stability of the inverted pendulum and Kapitsa’s sewing machine
• Chapter 16. Space flight of a photo camera cap
• Chapter 17. The angular velocity of a clock hand and Feynman’s “self-propagating pseudoeducation”
• Chapter 18. Planetary rings
• Chapter 19. Symmetry (and Curie’s principle)
• Chapter 20. Courant’s erroneous theorems
• Chapter 21. Ill-posed problems of mechanics
• Chapter 22. Rational fractions of flows
• Chapter 23. Journey to the center of the earth
• Chapter 24. Mean frequency of explosions (according to Ya. B. Zel’dovich) and de Sitter’s world
• Chapter 25. The Bernoulli fountains of the Nikologorsky bridge
• Chapter 26. Shape formation in a three-liter glass jar
• Chapter 27. Lidov’s moon landing problem
• Chapter 28. The advance and retreat of glaciers
• Chapter 29. The ergodic theory of geometric progressions
• Chapter 30. The Malthusian partitioning of the world
• Chapter 31. Percolation and the hydrodynamics of the universe
• Chapter 32. Buffon’s problem and integral geometry
• Chapter 33. Average projected area
• Chapter 34. The mathematical notion of potential
• Chapter 35. Inversion in cylindrical mirrors in the subway
• Chapter 36. Adiabatic invariants
• Chapter 37. Universality of Hack’s exponent for river lengths
• Chapter 38. Resonances in the Shukhov tower, in the Sobolev equation, and in the tanks of spin-stabilized rockets
• Chapter 39. Rotation of rigid bodies and hydrodynamics

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