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| Stillwell J. — Yearning for the Impossible: The Surprising Truths of Mathematics |
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| Предметный указатель |
Elliptic modular function 195
Empyrean 103
Equal temperament 20 21
Equality and adequality 91
Equality by cutting and pasting 11 78
Equality of areas 10
Equality of polygons 78
Equations, cubic 30
Equations, linear 88 127
Equations, quadratic 29 88
Equidistant curve 124
Equivalence classes 186
Equivalence classes and lattices 193
Equivalence classes as infinite sets 208
Equivalence classes as points on 2-torus 193
Equivalence classes as points on a surface 195
Equivalence classes, addition of 186
Escher, Maurits Cornelius, Circle Limit IV 122
Escher, Maurits Cornelius, longing for the impossible 178
Escher, Maurits Cornelius, Waterfall 177
Euclid and distributive law 28
Euclid and parallel axiom 50 71 101
Euclid and volume of tetrahedron 81
Euclid, approach to primes 155
Euclid, axioms for geometry 126
Euclid, Elements 12 50
Euclid, proof of infinitude of primes 159
Euclid, unstated assumptions 126
Euclidean algorithm 16
Euclidean algorithm and gcd 16
Euclidean algorithm on  and 1 17
Euclidean algorithm, running forever 16 18
Euclidean geometry 114 125
Euclidean geometry and Kant 125
Euclidean geometry and Klein 126
Euclidean geometry and linear algebra 127
Euclidean geometry and parallels 114
Euclidean line 127
Euclidean plane 101 114
Euclidean space 126 132
Euclidean space of dimension n 135
Euclidean space, assumed by Beltrami 125
Eudoxus 13
Eudoxus and gaps in the rationals 201
Eudoxus, method of exhaustion 86
Euler, Leonhard 43
Euler, Leonhard, and complex integers 155
Euler, Leonhard, and the four-square identity 141
Euler, Leonhard, Elements of Algebra 170
Euler, Leonhard, introduced complex integers 163
Euler, Leonhard, solution of  170
Exponential function 43
Fermat, Pierre de and adequality 91
Fermat, Pierre de and conic sections 88
Fermat, Pierre de, claim about  170
Fermat, Pierre de, coordinate geometry 51 71
Fermat, Pierre de, last theorem 171
Fermat, Pierre de, theorems 155
Ferrari, Lodovico 41
fibonacci 35
Fifth (musical interval) 2
Finite proofs 198
Finite universe 104 198
Flatness 101 102 108
Flatness and angle sum 114
Flatness and Gaussian curvature 117
Flatness of cylinder 109 182
Fluxions 99
Four-square identity and multiplicative absolute value 140
Four-square identity, encapsulates quaternions 140
Four-square theorem 139
Fourier, Joseph 191
Fourth (musical interval) 2
Fourth dimension xi 129 136
Franklin, Benjamin 156
frequency 3
Frequency and pitch 3
Frobenius, Georg 140
Function 99
Function of time 100
Function, circular 190
Function, complex 191
Function, constant 100
Function, elliptic 191
Function, elliptic modular 195
Function, exponential 43
Function, periodic 190
Fundamental theorem of algebra 41
Fundamental theorem of calculus 96
Galileo Galilei 34
gaps 201
Gauss, Carl Friedrich 38
Gauss, Carl Friedrich, and elliptic functions 191
Gauss, Carl Friedrich, and fundamental theorem of algebra 42
Gauss, Carl Friedrich, and non-Euclidean geometry 115
Gauss, Carl Friedrich, and non-Euclidean periodicity 194
Gauss, Carl Friedrich, and quaternions 141 144
Gauss, Carl Friedrich, and surface curvature 114
Gauss, Carl Friedrich, angle sum theorem 112
Gauss, Carl Friedrich, complex two-square identity 141
Gauss, Carl Friedrich, introduced Gaussian integers 163
Gauss, Carl Friedrich, on infinity 199
Gauss, Carl Friedrich, surveying 109
GCD 16 160
gcd of complex integers 173
gcd of complex primes 155
gcd of integers 160
General relativity 127 213
Geodesies 109
Geodesies on cylinder 109
Geodesies on sphere 111
Geodesies, behavior of 109
Geodesies, mapped to lines 119
Geometric series 83
Geometric series and the evaluation of n 96
Geometry of constant curvature 127
Geometry of Euclid 12 73 125
Geometry of negative curvature 126
Geometry of zero curvature 126
Geometry, algebraic 87
Geometry, arithmetization of 126
Geometry, axiom systems 126
Geometry, coordinate 51 71 87
Geometry, dimension of 127
Geometry, Euclidean 114 125
Geometry, Euclidean plane 114
Geometry, Euclidean plane, holds on horosphere 116
Geometry, Euclidean, and parallels 114
Geometry, four-dimensional 129
Geometry, hyperbolic 116 195
Geometry, hyperbolic, and parallel axiom 126
Geometry, incidence 60
Geometry, infinitesimal 85
Geometry, non-Euclidean 101 114 119 126
Geometry, projective 61
Geometry, projective, axioms 76
Geometry, spherical 111 112 116
Geometry, spherical, formula for circumference 116
Geometry, spherical, in non-Euclidean space 116
Geometry, split with number theory 12
Girard, Albert 41
Global positioning systems 125 127
Goedel, Kurt 212
Graves, John 140
Graves, Robert 55
Gravity 127
Great circle 109
Great circle, projected to line 119
Greatest common divisor see gcd
Greene, Brian 190 213
| Gunn, Charlie 124
Hadamard, Jacques 41 156 211
Hamilton, William Rowan 130
Hamilton, William Rowan, abandoned commutative law 136
Hamilton, William Rowan, and space rotations 144
Harnack, Adolf 202
Harriot, Thomas 107
Harriot, Thomas, angle sum theorem 112
Helix 110
Hermite, Charles 207
Hilbert, David 68
Hilbert, David, and area of polygons 79
Hilbert, David, and mathematical existence 212
Hilbert, David, and the Desargues theorem 72
Hilbert, David, Geometry and the Imagination 151
Hilbert, David, Grundlagen dei Geometrie 126
Hilbert, David, Mathematical Problems 212
Hipparchus 107
Hobbes, Thomas 98
Hobbes, Thomas, attempt to square the circle 99
Holmes, Oliver Wendell 69
Holmes, Sherlock 86
Horizon 47
Horosphere 116
Hyperbolic cosine 116
Hyperbolic geometry 116 195
Hyperbolic geometry and axiom systems 126
Hyperbolic geometry and parallel axiom 126
Hyperbolic plane 116 119 121
Hyperbolic plane, model of 121
Hyperbolic plane, tilings of 195
Hyperbolic sine 116
Hyperbolic space 123 189
icosahedron 144
Icosahedron symmetry 146
Ideal 172 173
Ideal as an infinite set 208
Ideal factor 173
Ideal number 173
Ideal points 48
Ideal product 175
Ideal, nonprincipal 174
Ideal, prime 155 172
Ideal, principal 173
Identity Law 70
Identity, additive 70
Identity, Diophantus 35
Identity, Diophantus, and multiplicative norm 167
Identity, eight-square 140
Identity, four-square 140
Identity, multiplicative 70 133
Identity, symmetry 147
Identity, three-square 132
Identity, two-square 34 130 140
Identity, two-square, complex 141
Imaginary xi
Imaginary number xi see
Impossibilities, actual 211
Impossibilities, apparent 211
Incidence and coincidence 61
Incidence axioms 60
Incidence geometry 60
Incommensurable 10
Indivisibles 98
Infinite decimals 15 209
Infinite decimals, introduced by Stevin 15
Infinite lines 50
Infinite object 198
Infinite processes 15 198
Infinite sequence 199
Infinite series for  208
Infinite set 197
Infinite space 102 198
Infinite sum 83
Infinite, completed 200
Infinitesimal 77
Infinitesimal as a figure of speech 99
Infinitesimal as a function of time 100
Infinitesimal calculus 87 100
Infinitesimal difference 90
Infinitesimal geometry 85
Infinitesimal line segments 126
Infinitesimal sectors 87
Infinitesimal slices 98
Infinity and infinitesimals 99
Infinity, actual 199 201 202
Infinity, line at 55
Infinity, perpendicular at 115
Infinity, points at 48 55
Infinity, potential 199 201
Inner product 76
INTEGER 26 155
Integer, complex 155
Integer, division property 159
Integer, Gaussian 163
Integer, Gaussian, division property 165
Integer, negative 26
Integer, point 51
Integer, positive 156
Integral sign 93
Inverse law 70
Inverse, additive 70 131
Inverse, multiplicative 70
Irrational xi
Irrational and decimal fractions 13
Irrational and ratio 1
Irrational angle 168
Irrational as a gap in the rationals 7 13
Irrational number xi
Irrational origin of word 9
Irrational points 197
Irrational roots of 2 162
Irrational triangles 7
Irrationality and Euclidean algorithm 18
Irrationality and theory of volume 11
Irrationality in geometry 10
Irrationality of  21
Irrationality of 9
Jacobi, Carl Gustav 195
Kant, Immanuel 125
Klein, Felix 125 195
Kolmogorov, Andrei Nikolaevich xi 211
Kummer, Ernst Eduard 155
Kummer, Ernst Eduard, and Fermat's last theorem 171
Kummer, Ernst Eduard, on imperfect complex integers 169
L'Hopital, Guillaume Francois Antoine 91
Lattice 164
Lattice and doubly periodic plane 192
Lattice of multiples 164 173
Lattice, shapes 193
Lattice, shapes, plane of 193
Laws of algebra 33 69
Laws of algebra and projective coincidences 72
Laws of algebra, associative 70
Laws of algebra, commutative 70
Laws of algebra, distributive 26 70
Laws of algebra, follow from Pappus theorem 75
Laws of algebra, identity 70
Laws of algebra, inverse 70
Legendre, Adrien-Marie 132 140
Leibniz, Gottfried Wilhelm 90 99
Leibniz, Gottfried Wilhelm, calculus notation 99
Leibniz, Gottfried Wilhelm, calculus of infinitesimals 100
Length and absolute value 35 38
Length and area of circle 85
Length and multiplication 63
Length in proof of Pappus theorem 63
Length of a countable set 203
Length of curves 77 191
Length of ellipse 191
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