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

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American Mathematical Society, Sep 4, 2014 - Mathematics - 167 pages

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.

 

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Contents

Chapter
1
Chapter
7
Rotation of a Liquid
33
What Force Drives a Bicycle Forward?
37
Hooke and Keplerian Ellipses and Their Conformal Transformations
39
The Stability of the Inverted Pendulum and Kapitsas Sewing Machine
45
Space Flight of a Photo Camera Cap
49
The Angular Velocity of a Clock Hand and Feynmans SelfPropagating Pseudoeducation
51
Mean Frequency of Explosions according to Ya B Zeldovich and de Sitters World
75
The Bernoulli Fountains of the Nikologorsky Bridge
79
Shape Formation in a ThreeLiter Glass Jar
83
Lidovs Moon Landing Problem
87
The Advance and Retreat of Glaciers
91
The Ergodic Theory of Geometric Progressions
99
The Malthusian Partitioning of the World
101
Percolation and the Hydrodynamics
103

Planetary Rings
55
Symmetry and Curies Principle
59
Courants Erroneous Theorems
61
IllPosed Problems of Mechanics
65
Rational Fractions of Flows
69
Journey to the Center of the Earth
71
Average Projected Area
111
Inversion in Cylindrical Mirrors in the Subway
127
Adiabatic Invariants
143
Universality of Hacks Exponent for River
153
Rotation of Rigid Bodies and Hydrodynamics
161
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