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Symmetry in Science and Art

Editat de A. Shubnikov
en Limba Engleză Paperback – 14 mar 2012
The perception of symmetry in art and in nature has been appreciated since antiquity, with development of the underlying laws tracing back at least to Pythagorean times. By the end of the eighteenth century it was realized that the immense variety of natural crystal shapes could be accounted for on the basis of a rather small number of symmetry operations, of which some were equally applicable to biological systems. The mathematical theory of symmetry continued to mature throughout the last century, culminating in the independent discoveries in Russia, Germany, and England that a total of only 230 independent ways exist in which the operations of rotation, reflection, and translation can be combined to transform three-dimensional geometrical objects into themselves. Derivation of the 230 space groups depends ultimately on restricting the meaning of symmetry to that of a property of purely geometrical figures. A. V. Shubnikov and his collaborators, over the past three decades, expanded this concept of symmetry to include the sign of transformation operations.
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Specificații

ISBN-13: 9781468420692
ISBN-10: 1468420690
Pagini: 460
Ilustrații: XXVI, 420 p. 443 illus., 34 illus. in color.
Dimensiuni: 152 x 229 x 24 mm
Greutate: 0.61 kg
Ediția:Softcover reprint of the original 1st ed. 1974
Editura: Springer Us
Colecția Springer
Locul publicării:New York, NY, United States

Public țintă

Research

Cuprins

1 Introduction • From Intuitive Concepts to the Definition of Symmetry.- 2 Symmetry of One-Sided Rosettes.- 3 Symmetry of Figures with a Singular Point.- 4 Symmetry of One-Sided Bands.- 5 Symmetry of Two-Sided Bands.- 6 Symmetry of Rods.- 7 Symmetry of Network Patterns • Two-Dimensional Continua and Semicontinua.- 8 Symmetry of Layers.- 9 Symmetry of Three-Dimensional Spaces • Discontinua and Continua.- 10 Elements of Group Theory • The Classical Crystallographic Groups.- 11 Groups of Generalized Symmetry • Antisymmetry and Colored Symmetry.- 12 Symmetry in Science and Art • Conservation Laws • Symmetrization and Dissymmetrization of Physical Systems • Principle of Symmetry for Composite Systems.- Resumé.