Fearful Symmetry: Is God a Geometer?Courier Corporation, 01.08.2010 - 287 Seiten This fascinating study explores a fundamental paradox behind the patterns of the natural world, in which symmetrical causes lead to asymmetrical effects. Lesser and greater patterns—the structure of subatomic particles, a tiger's stripes, the shapes of clouds, and the vibrations of the stars—are produced by broken symmetry. This accessible exploration of the physical and biological world employs the mathematical concepts of symmetry to consider the deepest questions of modern physics. An active popularizer of mathematics, Ian Stewart is a university professor and former columnist for Scientific American's "Mathematical Games" column. Martin Golubitsky is Distinguished Professor of Mathematics and Physical Sciences at the Ohio State University, where he serves as Director of the Mathematical Biosciences Institute. Both authors share an interest in the application of new mathematical ideas to scientific problems. More than 120 figures illustrate their illuminating survey of the interaction of symmetry with dynamics and the mathematical unity of nature's patterns. |
Inhalt
What Is Symmetry? | 26 |
Where Did It Go? | 54 |
Forever Stones | 73 |
Striped Water | 104 |
The Universe and Everything | 127 |
Turings Tiger | 149 |
The Pattern of Tiny Feet | 189 |
Icons of Chaos | 222 |
Well Is She? | 243 |
Further Reading | 270 |
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angle animal atoms axis basic Bénard convection bifurcation diagram bilateral symmetry blastula blobs break broken symmetry buckling cells centre chaos chapter chemical circles circular symmetry Couette flow Couette-Taylor flow creatures crystals cube Curie's Principle cylinder disc droplets dynamics effect exactly example Figure fluid forces fundamental gaits galaxies Gastrulation geometry glide reflections half a period Hopf bifurcation human idea identical kind legs move logistic equation look mathematical mathematicians mechanics mirror molecules morphogenesis nature observed occur oscillators particles patterns phase physical ping-pong ball plane possible precisely problem pronk quantum reflectional symmetry regular result right-handed rigid motions rotational symmetry sequence shape space speed sphere spherical spiral square starfish stars structure symme symmetrically related symmetry group symmetry-breaking Taylor vortices theory there's tions transformations translations transverse gallop trot turbulent Taylor vortices Turing Turing's types universe unstable wave wavy vortices