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Weyl H. — Symmetry
Weyl H. — Symmetry

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Название: Symmetry

Автор: Weyl H.

Аннотация:

Symmetry is one of the ideas by which man through the ages has tried to comprehend and create order, beauty, and perfection. Starting from the concept that symmetry equals harmony of proportions, this book gradually develops first the geometric concept of symmetry in its several forms as bilateral, translatory, rotational, ornamental, and crystallographic symmetry, and finally rises to the general abstract mathematical idea underlying all these special forms.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1982

Количество страниц: 176

Добавлена в каталог: 24.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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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