Softcover ISBN:  9781470417017 
Product Code:  MBK/85 
List Price:  $31.00 
MAA Member Price:  $27.90 
AMS Member Price:  $24.80 
Electronic ISBN:  9781470418892 
Product Code:  MBK/85.E 
List Price:  $29.00 
MAA Member Price:  $26.10 
AMS Member Price:  $23.20 

Book Details2014; 167 ppMSC: 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, TelAviv University
ReadershipAll mathematicians and physicists, graduate and undergraduate students interested in Arnold's unique style of explaining natural (mainly physics) phenomena.

Table of Contents

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 “selfpropagating pseudoeducation”

Chapter 18. Planetary rings

Chapter 19. Symmetry (and Curie’s principle)

Chapter 20. Courant’s erroneous theorems

Chapter 21. Illposed 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 threeliter 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 spinstabilized rockets

Chapter 39. Rotation of rigid bodies and hydrodynamics


Additional Material

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.
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


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 Book Details
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 Reviews

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 Get Permissions
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, TelAviv 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 “selfpropagating pseudoeducation”

Chapter 18. Planetary rings

Chapter 19. Symmetry (and Curie’s principle)

Chapter 20. Courant’s erroneous theorems

Chapter 21. Illposed 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 threeliter 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 spinstabilized 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.
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