Mathematical understanding of nature : essays on amazing physical phenomena and their understanding by mathematicians
著者
書誌事項
Mathematical understanding of nature : essays on amazing physical phenomena and their understanding by mathematicians
American Mathematical Society, c2014
- : [pbk.]
- タイトル別名
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Математическое понимание природы
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注記
"Originally published in Russian by МЦНМО under the title Математическое понимание природы, c2011"--T.p. verso
内容説明・目次
内容説明
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.
目次
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
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