"This text is for a one-semester undergraduate course on geometry. It is richly illustrated and contains hundreds of exercises."--BOOK JACKET.
With that principle as the starting point, Barker and Howe begin an insightful and rewarding study of Euclidean geometry. The primary focus of the book is on transformations of the plane.
Starting at an elementary level, this book explains the computational techniques such as rotation invariance, irreducible tensor operators, the Wigner—Eckart theorem, and Lie groups that are necessary to understand nuclear physics, ...
... Nonlinear Evolution Equations and Dynamical Systems NEEDS'92 (Dubna, Russia, 6–17 July 1992, (V. Makhankov, I ... waves in integrable and nonintegrable systems, Mathematical Modeling and Com- putation, vol. 16, Society for Industrial and ...
15 Breaking of Continuous Symmetries. Goldstone's Theorem For a long time, the mechanism of spontaneous breaking of continuous symmetries has been recognized to be at the basis of many collective phenomena and in particular of phase ...
With the circle, any rotation will do—even by 0.000000001 degrees of rotation—is a symmetry operation of the circle. ... Because continuous symmetry groups have an infinite number of symmetry operations, or elements, we cannot write ...
In general it is very difficult to calculate the continuous symmetry of a figure. The continuous symmetry of some well-known figures is given in the previous paper, “Examples of Measuring Continuous Symmetry,” and repeated here: Figure ...
This book discusses the origins of ornamental art -- illustrated by the oldest examples, dating mostly from the paleolithic and neolithic ages, and considered from the theory-of-symmetry point of view.
This book is a comprehensive introduction to the application of continuous symmetries and their Lie algebras to ordinary and partial differential equations.
... symmetries. Continuous symmetry is invariance under continuous transformation. An example of a continuous transformation would be the rotation of a circle. Since the appearance of a circle does not change under continuous rotations, we ...
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