SymmetryPrinceton University Press, 1952 - 168 Seiten Symmetry is a classic study of symmetry in mathematics, the sciences, nature, and art from one of the twentieth century's greatest mathematicians. Hermann Weyl explores the concept of symmetry beginning with the idea that it represents a harmony of proportions, and gradually departs to examine its more abstract varieties and manifestations—as bilateral, translatory, rotational, ornamental, and crystallographic. Weyl investigates the general abstract mathematical idea underlying all these special forms, using a wealth of illustrations as support. Symmetry is a work of seminal relevance that explores the great variety of applications and importance of symmetry. |
Inhalt
Bilateral Symmetry | 3 |
Translatory rotational and related symmetries | 41 |
Ornamental symmetry | 83 |
Crystals The general mathematical idea of symmetry | 119 |
Determination of all finite groups of proper rotations in 3space | 149 |
Inclusion of improper rotations | 155 |
Acknowledgments | 157 |
| 161 | |
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a₁ affine geometry algebraic angle arbitrary atoms automorphisms axes axis band ornaments basic bilateral symmetry body C₁ C₂ called carries Cartesian cells circle configuration congruences consists contains coordinate system coordinates x1 crystals cyclic group D₁ determined dimensions dodecahedron double infinite rapport e₁ enantiomorph equal equation equivalent figure finite groups form a group geometric group of automorphisms groups of proper groups of rotations Hence hexagonal horizontal identity improper rotations indiscernible instance invariant lattices inverse iteration laevo lattice basis laws lecture left and right Leibniz linear transformations mathematical metric ground form metry motion nature octahedron operations organic orthogonal pentagon phyllotaxis plane pole of multiplicity Polykleitos positive possible problem proper congruences proper rotations quadratic forms rational numbers real numbers reflection regular respect rotational symmetry screw sides sphere structure of space Studium Generale subgroup theory tion translation translatory two-dimensional vectors e1 vertical