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| Weyl H. — Symmetry |
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| Предметный указатель |
'Spiral' symmetry 70
A priori statements and symmetry 126
Absolute vs. relative space and time 21
Abstract group 145
Active (optically active) substances 17 29
ADAM and EVE 32
Addition of vectors 93
Affine geometry 96 132
Algebra 121 135
Alhambra (Granada) 109 112
Analytic geometry 94
Angraecum distichum 51
Arabian Nights 90
Archibald, R.C. 72
Archimedes 92
Aristotle 3
Arithmetical theory of quadratic forms 120
Arrangement of atoms in a crystal 122
Ascaris megalocephala 36
Associative law 95
Asymmetry and symmetry in art 13 16
Asymmetry and the origin of life 32
Asymmetry in the animal kingdom 26
Asymmetry of crystals 17 29
Asymmetry the prerogative of life? 31
Aurea sectio 72
Automorphism 18 42
Automorphism for any structure-endowed entity 144
Automorphism in algebra 137
Axis 109 149
Balmer series 133
Band ornaments 48—51
bar 52
Beauty and symmetry 3 72
Bees, their geometric intelligence 91
Beethoven (pastoral sonata) 52
Bilateral symmetry 3
Bilateral symmetry of animals 26
Bilateral symmetry of the human body 8
Bilateral symmetry, aesthetic and vital value 6 28
Bilateral symmetry, definition 4
Bipotentiality of plasma 38
Birkhoff, G.D. 3 53
Bonnet, Charles 72
Buridan's ass 19
Capella Emiliana (Venice) 65
Cartesian coordinates 97
Causal structure 25 132
Central symmetry, in three dimensions 79—80
Central symmetry, in two dimensions 65
Chartres 16
Chinese window lattice 113
Church, A.H. 73
Clarke 20
Class of crystals 122
Class of equivalent points 150
Cohn-Vossen, S. 90
Commensurable 75
Commensurable and incommensurable 135
Commutative law (in general not valid for composition of transformations) 41
Commutative law for addition of vectors 93
complex numbers 136
Composition of elements in an abstract group 145
Composition of mappings 41
Congruence and congruent transformations 18 43 130
Conklin 34
Constitution and environment 126
Construction of 17-gon by ruler and compass 139 141
Contingency (and lawfulness) 26
Continuity, analysis of 136
Continuous group and discontinuous subgroup 68—69
Continuous vs. discontinuous features 108—109 127
Coordinates and coordinate system 94
Corneto 13
Cosmati 49
Crystals 28
Crystals, crystallographic groups 120
Crystals, for any number of dimensions 121
cube 74
Cyclic group 65
da Vinci, Leonardo 66 99
Darwin, Charles 92
de Beer, G.R. 34
Densest packing of circles 83
Densest packing of spheres 90
Descartes 95
Determination of left and right in animals 33—38
Dextro- and laevo-forms of crystals 29
Diamond lattice 102
Diatoms 87
Dickson, L. 121
Dihedral group 65
Dilatation and 'dilatory' symmetry 68
Diodore 3
Dirichlet, Lejeune 121
Discontinuous group 68 99
Discontinuous group of translations 99—100 see
Distributive law 95
dodecahedron 74
Double infinite rapport 100
Driesch, Hans 35
Duerer 3 65
Dye, Daniel Sheets 113
Dynamic symmetry 72
Echinoderms 60
Einstein, Albert 130 132
Enantiomorph crystals 28
Entemena, King 8
Epicurus 128
Equiangular spiral 69
Equivalence of left and right 19—20 129
Equivalence of past and future 24
Equivalence of positive and negative electricity 25
Equivalent points 150
Euclid 17 74
Eudoxus 136
Euler, L. 149
Euler, L., his topological formula ("polyhedron formula") 89
Exclusion principle 134
Faistauer, A. 24
Faust 45
Fedorow 92
Fibonacci series 72
Field of numbers 143
Flowers, their symmetry 58
Fontenelle 91
Frey, Dagobert 16
Fugus 34
future see "Past"
Galen 4
Galois, E., Galois group and Galois theory 137 142
Gauss 120 139 142
General relativity theory 132
Genetic constitution 37
Genotype and phenotype 126
Genotypical and phenotypical inversion 37
Geometric and physical automorphism 129—130
Geometric automorphism 130
Geometry, what is a geometry? 133
Geranium 66
Gliding axis 109
Goethe 51 72
Group of automorphisms 42 144
Group of dilatations 68
Group of permutations 135
Group of proper and improper rotations 65
Group of transformations 43
Group, abstract group 145
Group, finite group of proper rotations in 2 dimensions 54
Group, finite group of unimodular transformations in 2 dimensions 107
| Group, in 3 dimensions 120
Group, such groups having an invariant lattice 120
Group, the same for 3 dimensions 79 149—154 80 120 155—156 120
Haeckel, Ernst 60 75 88
Hambidge, J. 72
Harrison, R.G. 35
Helianthus maximus 70 73
Helix 71
Helladic 12
Helmholtz, H. 18 43 128
Heraldic symmetry 8
hermite 121
Herzfeld, Ernst 10
Hexagonal lattice or pattern 83 110
Hexagonal symmetry 63
Hilbert, D. 90
Historic asymmetry 16
Hodler, F. 16
Homo sapiens 30
Homogeneous linear transformation 96
Honey-comb 83 90—91
Huxley, Julian S. 34
Hypercomplex number system 121
icosahedron 74
Identity 41
Indiscernible 17 127
Infinite rapport 47
Invariant quadratic form 106 108
Invariant quantities, relations, etc. 133
Inverse mapping 41
Inversion of left and right 23
Inversion of time 24 52
Inversion, situs inversus 30
Irrationality of square root of two 129
Jaeger, F.M. 29
Japp, F.R. 31
Jones, Owen 113
Jordan, Pascual 32
Kant, I. 21 130
Kelvin, Lord 93
Kepler 76 90
Klein, Felix 133
Koenig, Samuel 91
Laevo- see under "Dextro-"
Lattice 100
Lattice basis 100
Lattice structure and metric structure 104
Lattice, rectangular and diamond lattices 102
Laue interference pattern or diagram 124
Law of rational indices 121
Left and right: polar opposites or not? 17 22
Left and right: polar opposites or not? concern a screw 17
Left and right: polar opposites or not? in paintings 23
Leibniz 17 18 20 21 27 127
Linear independence of vectors 94
Linear transformation, homogeneous 96
Linear transformation, non-homogeneous 97
Logarithmic spiral 69
longitudinal reflection 50
Lorentz group 131
Lorentz, H.A. 131
Lorenz, Alfred 52
Ludwig, W. 26 38
Mach, Ernst 19
Macroscopic and microscopic symmetry of crystals 123
Magnetism, positive and negative? 20
Mainz cathedral 56
Mann, Thomas 64
Mapping 18 41
Maraldi 90 91
Maschke, H. (and Maschke's theorem) 107
Medusa 66
Medusae 63
Metric ground form 96
Metric structure and lattice structure 104
Michelangelo 22
Minkowski, H. 90 121
Mitosis 34
Modul 96
Monreale 14
Morphology 109 126
Motion (in the geometric sense) 44
Multiplication of a vector by a number 94
Music, formal elements of 52
Mythical thinking 22
Nautilus 70
Needham, Joseph 34
Negative see under "Positive"
Newton 20 27 43
Nicomachean Ethics 4
Niggli, Paul 122
Objective statements 128
octahedron 74
One-dimensional reflection 47
Ontogenesis of bilateral symmetry (and asymmetry) 33
Oppe, Paul 24
Optically active 17
Order of a group 79
Ornamental symmetry in one dimension 48
Ornamental symmetry in two dimensions 99—115
Orthogonal transformation 97
Orthogonally equivalent 99
Parenchyma of maize 87
Particle (and wave) 25
Past and Future 24 132
Pasteur 29—31
Pauli, W. 134
Penicillium glaucum 30
Pentagonal symmetry in organic nature 63
Pentagram 45
Permutation 134
Phenotypical inversion 37
Phenylketonuria 30
Phyllotaxis 72
Phylogenesis of asymmetry 33
Physical automorphism 129
Pisa Baptisterium 55
Planck, Max 133
Planetary orbits and the regular polyhedra 76
Plato 8 28 73
Plato, his Timaeus 74
Plato, platonic solids 73
Polar axis 33
Polar polyhedra 78
Polarity see under "Equivalence"
Pole 109 149
Pole, animal and vegetative poles of blastula 33
Pole, magnetic poles 19
Polyhedral groups 78 154
Polykleitos 3 65
Positive and negative electricity 24
Positive and negative magnetism 20
Potentially infinite 51
probability 25
Projective geometry 132
Proper and improper congruences 43
Prospective potency and significance 35
Pythagoras' theorem 96
Quadratic forms 96 108
Quadratic forms, their arithmetical theory 120
Quantum physics 25 133
Quincunx 64 103
Racemic acid 29
Radiolarians 76 88
Raphael (Sistine Madonna, tapestry cartoons) 23
Reaumur 91
Rectangular lattice 102
Reflection 4
Reflection and rotation by 180° 9 77
Reflection at origin 79
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