Arnold, V. I
Mathematical understanding of nature Essays on amazing physical phenomena and their understanding by mathematicians - Indian Edition - Providence, Rhode Island American Mathematical Society (AMS) 2023 - xiv, 167 p
1. The eccentricity of the Keplerain orbit of Mars
2. Rescuing the Empennage
3. Return along a Sinusoid
4. The Dirichlet Integral and the Laplace Operator
5. Snell's Law of refraction
6. Water depth and Cartesian science
7. A drop of water refracting light
8. Maximal deviation angle of a beam
9. The rainbow
10. Mirages
11. Tides, Gibbs Phenomenon, and Tomography
12. Rotation of a liquid
13. What force drives a bicycle forward? 14. Hooke and Keplerain Ellipses and their conformal transformations
15. The stability of the inverted pendulum and Kapitsa's sewing machine
16. Space flight of a photo camera cap
17. The angular velocity of a clock hand and Feynman's "Self-Propagating Pseudoeducation"
18. Planetary rings
19. Symmetry (and Curie's Principle)
20. Courant's Erroneous Theorems
21. Ill-posed problems of mechanics
22. Rational fractions of flows
23. Journey to the center of the Earth
24. Mean frequency of explosion (according to Ya. B. Zel'dovich) and de Sitter's world
25. The Bernoulli Fountains of the Nikologorsky Bridge
26. Shape formation in a three-liter glass jar. 27. Lidov's moon landing problem
28. The advance and retreat of glaciers
29. The Ergodic Theory of geometric progressions
30. The Malthusian partitioning of the world
31. Percolation and the Hydrodynamics of the Universe
32. Buffon's problem and integral geometry
33. Average projected area
34. The mathematical notion of a potential
35. Inversion in cylindrical mirrors in the subway
36. Adiabatic invariants
37. Universality of Hack's Exponent for river lengths
38. Resonances in the Shukhov Tower, in the Sobolev Equation, and in the Tanks of Spin-Stabilized Rockets
39. Rotation of rigid bodies and hydrodynamics
"This collection of 39 short stories gives the reader a unique opportunity to take a look at the scientific philosophy of Vladimir Arnold, one of the most original contemporary researchers. Topics of the stories included range from astronomy, to mirages, to motion of glaciers, to geometry of mirrors and beyond. In each case Arnold's explanation is both deep and simple, which makes the book interesting and accessible to an extremely broad readership. Original illustrations hand drawn by the author help the reader to further understand and appreciate Arnold's view on the relationship between mathematics and science.""
9781470438388 (PB)
Fluid mechanics Instructional exposition (textbooks, tutorial papers, etc.)
5 / ARN
Mathematical understanding of nature Essays on amazing physical phenomena and their understanding by mathematicians - Indian Edition - Providence, Rhode Island American Mathematical Society (AMS) 2023 - xiv, 167 p
1. The eccentricity of the Keplerain orbit of Mars
2. Rescuing the Empennage
3. Return along a Sinusoid
4. The Dirichlet Integral and the Laplace Operator
5. Snell's Law of refraction
6. Water depth and Cartesian science
7. A drop of water refracting light
8. Maximal deviation angle of a beam
9. The rainbow
10. Mirages
11. Tides, Gibbs Phenomenon, and Tomography
12. Rotation of a liquid
13. What force drives a bicycle forward? 14. Hooke and Keplerain Ellipses and their conformal transformations
15. The stability of the inverted pendulum and Kapitsa's sewing machine
16. Space flight of a photo camera cap
17. The angular velocity of a clock hand and Feynman's "Self-Propagating Pseudoeducation"
18. Planetary rings
19. Symmetry (and Curie's Principle)
20. Courant's Erroneous Theorems
21. Ill-posed problems of mechanics
22. Rational fractions of flows
23. Journey to the center of the Earth
24. Mean frequency of explosion (according to Ya. B. Zel'dovich) and de Sitter's world
25. The Bernoulli Fountains of the Nikologorsky Bridge
26. Shape formation in a three-liter glass jar. 27. Lidov's moon landing problem
28. The advance and retreat of glaciers
29. The Ergodic Theory of geometric progressions
30. The Malthusian partitioning of the world
31. Percolation and the Hydrodynamics of the Universe
32. Buffon's problem and integral geometry
33. Average projected area
34. The mathematical notion of a potential
35. Inversion in cylindrical mirrors in the subway
36. Adiabatic invariants
37. Universality of Hack's Exponent for river lengths
38. Resonances in the Shukhov Tower, in the Sobolev Equation, and in the Tanks of Spin-Stabilized Rockets
39. Rotation of rigid bodies and hydrodynamics
"This collection of 39 short stories gives the reader a unique opportunity to take a look at the scientific philosophy of Vladimir Arnold, one of the most original contemporary researchers. Topics of the stories included range from astronomy, to mirages, to motion of glaciers, to geometry of mirrors and beyond. In each case Arnold's explanation is both deep and simple, which makes the book interesting and accessible to an extremely broad readership. Original illustrations hand drawn by the author help the reader to further understand and appreciate Arnold's view on the relationship between mathematics and science.""
9781470438388 (PB)
Fluid mechanics Instructional exposition (textbooks, tutorial papers, etc.)
5 / ARN