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| Stillwell J. — Yearning for the Impossible: The Surprising Truths of Mathematics |
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| Предметный указатель |
Length, constructible 207
Length, hyperbolic 123
Leverrier, Urbain lean Joseph 33
LIMIT 90 99
Limit and properties of U 208
Limit of a ratio 99
Limit of a sum 100
Lindemann, Ferdinand 207 208
Line as a set of points 197
Line, asymptotic 115
Line, asymptotic, on pseudosphere 119
Line, Dedekind definition 202
Line, equation of 53 88
Line, Euclidean 127
Line, non-Euclidean 115
Line, nonstandard 125
Line, real number 26
Line, slope of 53
Liouville, Joseph 206
Little Desargues theorem 66
Lobachevsky, Nikolai 115
Lobachevsky, Nikolai Ivanovich 119 125
Local and global 180
Lowenheim, Leopold 212
Lucretius 102 103 198
Machin, John 84
Magnitudes 10
Magnitudes as numbers 12
Magritte, Rene 183
Manifolds 188
Method of exhaustion 86
Minding, Ferdinand 119
Model of consistent sentences 212
Model of hyperbolic plane 121
Model, conformal 122
Model, half-plane 123
Model, Klein construction 125
Model, projective 121 123 127
Moonshine 213
Motion 200
Moufang, Ruth 66 69
Moufang, Ruth, and little Desargues theorem 72
Multiplication in projective geometry 72
Multiplication in proof of Pappus theorem 63
Multiplication of lengths 63
Multiplication of negative numbers 26
Multiplication of quaternions 138
Multiplication, audible 37
Multiplication, audible and visible 38
Multiplication, geometry of 36 193
Multiplication, induces rotation 38
Multiplication, perceived as addition 4
Multiplication, visible 37
Multiplicative, absolute value 35 129 130
Multiplicative, absolute value, and four-square identity 140
Multiplicative, absolute value, for quaternions 131
Multiplicative, identity 70 133
Multiplicative, inverse 70
Multiplicative, norm 166
Musical intervals 2
Nahin, Paul 43
Needham, Joseph 22
Needham, Tristan 43
Neptune 33
Newton, Isaac 44 62 99
Newton, Isaac, and motion 200
Newton, Isaac, and tractrix 118
Newton, Isaac, definition of curvature 116
Nicomachus 2
Non-Euclidean circle 116
Non-Euclidean cylinder 119
Non-Euclidean geometry 101 114 119 126
Non-Euclidean geometry and Kant 125
Non-Euclidean line 115
Non-Euclidean periodicity 189 193 195
Non-Euclidean plane 116 119 125
Non-Euclidean plane, called hyperbolic 121
Non-Euclidean space 116
Nonstandard analysis 91 100
Norm of complex integers 170
Norm of Gaussian integer 166
Norm, multiplicative property 166
Number line 25 26
Number theory 12
Numbers and magnitudes 12
Numbers, algebraic 205
Numbers, algebraic, form a countable set 200 206
Numbers, complex 25
Numbers, complex, and rotations 141
Numbers, complex, arithmetic of 34
Numbers, complex, as pairs 130
Numbers, complex, in geometry 127
Numbers, complex, plane of 37
Numbers, complex, rational 30
Numbers, constructible 208
Numbers, hypercomplex 45
Numbers, ideal 173
Numbers, ideal, represented by infinite sets 198
numbers, imaginary xi 25 27 29
Numbers, imaginary, and quadratic equations 29
Numbers, irrational xi 12 99 162
Numbers, irrational, as gaps 202
Numbers, irrational, in China 22
Numbers, irrational, set of 201
Numbers, natural 1 155 156 197 199
Numbers, natural, in Elements 12
Numbers, natural, in geometry 6
Numbers, natural, set of 199
numbers, negative 25 26
Numbers, nonalgebraic 197
Numbers, normal 209
Numbers, prime 12 76 155
Numbers, rational 10
Numbers, rational, as periodic decimals 20
Numbers, rational, form a countable set 200
Numbers, real 27 127
Numbers, real, almost all irrational 203
Numbers, real, almost all normal 209
Numbers, real, almost all transcendental 207
Numbers, three-dimensional? 127
Numbers, transcendental xi 206
Numbers, two-dimensional 129
octahedron 144
Octahedron symmetry 145
Octave (musical interval) 2
Octave (musical interval) in the universe? 189
Octave (musical interval), division of 162
Octave (musical interval), non-Euclidean 189 193 195
Octave (musical interval), one-dimensional 190
Octonions 140
Origin 51 87
Pappus 63
Pappus theorem 63
Pappus theorem as an axiom 65
Pappus theorem, proof 64
parabola 87 88
Parallel axiom 49 101
Parallel axiom and angles 50
Parallel axiom and coordinates 51 71
Parallel axiom of Bolyai and Lobachevsky 126
Parallel axiom of Euclid 126
Parallel axiom, consequences 50 110
Parallel axiom, independence 125
Parallel axiom, separates geometries 126
Parallel lines 49
Parallel lines and Euclidean geometry 114
Parallel lines and vision 54
Parallel lines have same slope 54
Parallel lines in hyperbolic plane 101
Parallel lines in projective plane 61
| Parallel lines meet on horizon 48
Parallel lines, axioms for 126
Parallelepiped 80
Pascal, Blaise 62
Pascal, Blaise, theorem 62
Pascal, Etienne 62
Pelerin, Jean 57
Penrose, Lionel 179
Penrose, Roger 179
Pentagons 124
Periodic functions 190
Periodic line 187
Periodic plane 181
Periodic plane of lattice shapes 193
Periodic space 177 188
Periodicity and topology 187
Periodicity in continued fractions 19
Periodicity in Euclidean algorithm 16 18
Periodicity in infinite decimals 19
Periodicity in the plane and space 182
Periodicity, double 191
Periodicity, history of 190
Perspective 47
Perspective, view of line 182
Piranesi, Giovanni Battista 179
Pitch 3
Plane of lattice shapes 193
Plane, doubly periodic 191
Plane, Euclidean 101 114
Plane, hyperbolic 101 119 121
Plane, hyperbolic, in Escher pictures 122
Plane, non-Euclidean 116 119
Plane, non-Euclidean, periodic 193
Plane, periodic 181
Plane, projective 61
Plane, rotation 141
Plimpton 322 6
Plimpton 322 and rational angles 168
Plimpton 322 and rational complex numbers 40
Poincare, Henri 127 195
Poincare, Henri, conjecture 195
POLYGONS 77
Polygons with two sides 177 181
Polygons, area of 77
Polygons, equality of 78
Polyhedra 77 129
Polyhedra, regular 144
Polyhedra, regular, in the Elements 144
Polyhedra, volume of 77
Polynomials 42 44
Polynomials and algebraic numbers 205
Polynomials, complex factors of 44
Polynomials, real factors of 44
Polytopes 129 151
Polytopes, regular 149
Prime 155 156
Prime, complex 155
Prime, divisor property 161
Prime, divisor property, failure 172
Prime, divisor property, Gaussian 168
Prime, factorization, existence 157
Prime, factorization, Gaussian 166
Prime, factorization, unique 155 157 167
Prime, Gaussian 163 166
Prime, ideal 155 172
Primum Mobile 103
Product of complex numbers 34
Product of four lengths 12
Product of ideals 175
Product of lengths 63
Product of numbers 10
Product of three lengths 11
Product of triangles 35
Product of two lengths 10
Product, inner 76
Projection 61
Projection, central 119
Projective configuration theorems 61
Projective explanation of coincidences 67 68
Projective explanation of coincidences and algebra 69
Projective geometry 61
Projective geometry and Klein 126
Projective geometry and linear algebra 127
Projective geometry, axioms 76
Projective model 121 127
Projective plane 61
Pseudodistance 121 125
Pseudosphere 118
Pseudosphere as hyperbolic cylinder 195
Pseudosphere, infinite lines on 119
Pseudosphere, mapped to disk 120
Pythagoras 2
Pythagorean comma 4
Pythagorean equation 5
Pythagorean Theorem 5
Pythagorean theorem and complex absolute value 38
Pythagorean theorem and parallel axiom 50 110
Pythagorean theorem and quaternion absolute value 139
Pythagorean theorem in Euclid 12
Pythagorean triples 6
Pythagoreans 2
Quadratic equation 29 88
Quadratic equation, discriminant of 30
Quadratic equation, imaginary solutions 30
Quadratic formula 30
Quadrivium 2
Quantum theory 213
Quartic equations 41
Quaternion 129
Quaternion as complex pair 141
Quaternion for space rotation 141 142
Quaternion, absolute value 131
Quaternion, absolute value, is multiplicative 139
Quaternion, multiplication 138
Quaternion, multiplication, is noncommutative 138
Quaternion, plaque 138
Quaternion, pure imaginary 143
Quaternion, representation of rotation 143
Quotient 159
Radicals 205
Raleigh, Walter 107
Rational angles 40 168
Rational numbers see numbers rational
Rational slopes 168
Recorde, Robert 9
Reductio ad absurdam 8
Regular polytopes in 151
Regular tilings 152
Regular tilings of 153
Remainder 159
Riemann, Bernhard 126 191
Rigid motion 133 136 142
Robinson, Abraham 100
Rodrigues, Olinde 141 144
Roots of 1 39
Rotation and roots of 1 39
Rotation of space 141
Rotation of tetrahedron 147
Rotation of the plane 38
Rotation, induced by multiplication 38 142
Rotation, quaternion representation of 143
Rotation, trivial 147
Ruler and compass construction 207
Saccheri, Girolamo 115
Saccheri, Girolamo, and the nature of lines 115 119
Saddle 117
Schlaefli, Ludwig 152
Second (musical interval) 4
Set of algebraic numbers is countable 206
Set of gaps 202
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