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

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Softcover ISBN: 978-1-4704-1701-7
Product Code: MBK/85
List Price: $31.00 MAA Member Price:$27.90
AMS Member Price: $24.80 Electronic ISBN: 978-1-4704-1889-2 Product Code: MBK/85.E List Price:$29.00
MAA Member Price: $26.10 AMS Member Price:$23.20
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List Price: $46.50 MAA Member Price:$41.85
AMS Member Price: $37.20 Click above image for expanded view Mathematical Understanding of Nature: Essays on Amazing Physical Phenomena and Their Understanding by Mathematicians Available Formats:  Softcover ISBN: 978-1-4704-1701-7 Product Code: MBK/85  List Price:$31.00 MAA Member Price: $27.90 AMS Member Price:$24.80
 Electronic ISBN: 978-1-4704-1889-2 Product Code: MBK/85.E
 List Price: $29.00 MAA Member Price:$26.10 AMS Member Price: $23.20 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$46.50 MAA Member Price: $41.85 AMS Member Price:$37.20
• Book Details

2014; 167 pp
MSC: Primary 70; 76; 78;

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

All mathematicians and physicists, graduate and undergraduate students interested in Arnold's unique style of explaining natural (mainly physics) phenomena.

• 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 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

• Reviews

• 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.

• 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
• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
2014; 167 pp
MSC: Primary 70; 76; 78;

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

All mathematicians and physicists, graduate and undergraduate students interested in Arnold's unique style of explaining natural (mainly physics) phenomena.

• 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 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
• 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.