MSC: Primary 70; 76; 78;
Print ISBN: 978-1-4704-1701-7
Product Code: MBK/85
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MAA Member Price: $27.90
Electronic ISBN: 978-1-4704-1889-2
Product Code: MBK/85.E
List Price: $29.00
AMS Member Price: $23.20
MAA Member Price: $26.10
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Mathematical Understanding of Nature: Essays on Amazing Physical Phenomena and Their Understanding by Mathematicians
Share this pageV. I. Arnold
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.
Arnold's talent for exposition shines in this collection of short chapters on a miscellany of topics. I could not stop reading until I reached the end of the book. This book will entertain and enrich any curious person, whether a layman or a specialist.
—Mark Levi, Penn State University, author of “The Mathematical Mechanic”
This book, which fits all mathematical ages, provides a glimpse into the “laboratory” of one of the most influential mathematicians of our time. Its genre is absolutely unique. A kaleidoscope of intriguing examples illustrating applications of mathematics to real life, intertwines with entertaining and often wildly funny mathematical anecdotes, as well as with profound insights into modern research areas. A brilliant informal exposition, complemented by artful drawings by the author, makes the book a fascinating read.
—Leonid Polterovich, Tel-Aviv University
Readership
All mathematicians and physicists, graduate and undergraduate students interested in Arnold's unique style of explaining natural (mainly physics) phenomena.
Reviews & Endorsements
The remarks provide a glimpse into the background of the history and the culture of science and humanity. This book will entertain and make the reader think. I recommend this fascinating book to any curious person.
-- László Csizmadia, ACTA Sci Math.
Examples teach no less than rules, and errors, more than correct but abstruse proofs. Looking at the pictures in this book, the reader will understand more than learning by rote dozens of axioms (even together with their consequences about what sea the Volga River falls into and what horses eat). Most essays in the book are quite short, and their level of difficulty varies significantly -- some require only knowledge of a high school mathematics and some may be viewed as a serious challenge even for an experienced mathematician. As most texts written by Arnold, the book under review is a quite demanding but very stimulating and inspiring reading featuring original author's illustrations.
-- Zentralblatt Math
This is a wonderful book for browsing, for anyone drawn to physical applications of mathematics or to Arnold himself and the breadth of his interests.
-- MAA Reviews
Table of Contents
Table of Contents
Mathematical Understanding of Nature: Essays on Amazing Physical Phenomena and Their Understanding by Mathematicians
- Cover Cover11
- Frontispiece ii3
- Title page iii4
- Contents v6
- Foreword ix10
- Preface xiii14
- Chapter 1. The eccentricity of the Keplerian orbit of Mars 116
- Chapter 2. Rescuing the empennage 318
- Chapter 3. Return along a sinusoid 520
- Chapter 4. The Dirichlet integral and the Laplace operator 722
- Chapter 5. Snell’s law of refraction 1126
- Chapter 6. Water depth and Cartesian science 1530
- Chapter 7. A drop of water refracting light 1732
- Chapter 8. Maximal deviation angle of a beam 1934
- Chapter 9. The rainbow 2136
- Chapter 10. Mirages 2540
- Chapter 11. Tide, Gibbs phenomenon, and tomography 2944
- Chapter 12. Rotation of a liquid 3348
- Chapter 13. What force drives a bicycle forward? 3752
- Chapter 14. Hooke and Keplerian ellipses and their conformal transformations 3954
- Chapter 15. The stability of the inverted pendulum and Kapitsa’s sewing machine 4560
- Chapter 16. Space flight of a photo camera cap 4964
- Chapter 17. The angular velocity of a clock hand and Feynman’s “self-propagating pseudoeducation” 5166
- Chapter 18. Planetary rings 5570
- Chapter 19. Symmetry (and Curie’s principle) 5974
- Chapter 20. Courant’s erroneous theorems 6176
- Chapter 21. Ill-posed problems of mechanics 6580
- Chapter 22. Rational fractions of flows 6984
- Chapter 23. Journey to the center of the earth 7186
- Chapter 24. Mean frequency of explosions (according to Ya. B. Zel’dovich) and de Sitter’s world 7590
- Chapter 25. The Bernoulli fountains of the Nikologorsky bridge 7994
- Chapter 26. Shape formation in a three-liter glass jar 8398
- Chapter 27. Lidov’s moon landing problem 87102
- Chapter 28. The advance and retreat of glaciers 91106
- Chapter 29. The ergodic theory of geometric progressions 99114
- Chapter 30. The Malthusian partitioning of the world 101116
- Chapter 31. Percolation and the hydrodynamics of the universe 103118
- Chapter 32. Buffon’s problem and integral geometry 107122
- Chapter 33. Average projected area 111126
- Chapter 34. The mathematical notion of potential 115130
- Chapter 35. Inversion in cylindrical mirrors in the subway 127142
- Chapter 36. Adiabatic invariants 143158
- Chapter 37. Universality of Hack’s exponent for river lengths 153168
- Chapter 38. Resonances in the Shukhov tower, in the Sobolev equation, and in the tanks of spin-stabilized rockets 155170
- Chapter 39. Rotation of rigid bodies and hydrodynamics 161176
- Back Cover Back Cover1184