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Mathematical Understanding of Nature By V. I. Arnold

Mathematical Understanding of Nature

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Mathematical Understanding of Nature Summary

Mathematical Understanding of Nature: Essays on Amazing Physical Phenomena and their Understanding by Mathematicians by V. 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, USA 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, Israel.

Customer Reviews - Mathematical Understanding of Nature

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Mathematical Understanding of Nature Reviews

"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

"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.
- Laszlo Csizmadia, ACTA Sci. Math

Table of Contents

  • The eccentricity of the Keplerian orbit of Mars
  • Rescuing the empennage
  • Return along a sinusoid
  • The Dirichlet integral and the Laplace operator
  • Snell's law of refraction
  • Water depth and Cartesian science
  • A drop of water refracting light
  • Maximal deviation angle of a beam
  • The rainbow
  • Mirages
  • Tide, Gibbs phenomenon, and tomography
  • Rotation of a liquid
  • What force drives a bicycle forward?
  • Hooke and Keplerian ellipses and their conformal transformations
  • The stability of the inverted pendulum and Kapitsa's sewing machine
  • Space flight of a photo camera cap
  • The angular velocity of a clock hand and Feynman's "self-propagating pseudoeducation"
  • Planetary rings
  • Symmetry (and Curie's principle)
  • Courant's erroneous theorems
  • Ill-posed problems of mechanics
  • Rational fractions of flows
  • Journey to the center of the earth
  • Mean frequency of explosions (according to Ya. B. Zel'dovich) and de Sitter's world
  • The Bernoulli fountains of the Nikologorsky bridge
  • Shape formation in a three-liter glass jar
  • Lidov's moon landing problem
  • The advance and retreat of glaciers
  • The ergodic theory of geometric progressions
  • The Malthusian partitioning of the world
  • Percolation and the hydrodynamics of the universe
  • Buffon's problem and integral geometry
  • Average projected area
  • The mathematical notion of potential
  • Inversion in cylindrical mirrors in the subway
  • Adiabatic invariants
  • Universality of Hack's exponent for river lengths
  • Resonances in the Shukhov tower, in the Sobolev equation, and in the tanks of spin-stabilized rockets
  • The theory of rigid body rotation and hydrodynamics

Additional information

Mathematical Understanding of Nature: Essays on Amazing Physical Phenomena and their Understanding by Mathematicians by V. I. Arnold
V. I. Arnold
Used - Very Good
American Mathematical Society
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
This is a used book - there is no escaping the fact it has been read by someone else and it will show signs of wear and previous use. Overall we expect it to be in very good condition, but if you are not entirely satisfied please get in touch with us.