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| Авторизация |
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| Goodman A.W. — The Pleasures of Math |
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| Предметный указатель |
Abscissa 117
Absolute value 22 23 118
Abundant number 205 (prob. 9)
Arithmetic mean 67—69
Arithmetic progression 31 (prob. 21)
Axioms 18
Axis 116 117
Axis of a cone 102
Axis of a parabola 107
Axis of symmetry 107 110 139 193
BASEBALL 188 (prob. 12)
Binomial coefficients 33—39 183
box 133 134 159 6)
Bridge 17 188
Bridge problem 142
Broken diagonal 46
Calculus 8 116 122
Cauchy's inequality 136
Cauchy, Augustin Louis 136
circle 193 (prob. 5)
Closed path 76
Coloring of maps 91—101
Combinations 178 182—185
Composite 162
Cone 102—106 110—115
Cone, cone angle 103
Conic sections 102—115 146—150
Convergent sequence 200
Convergent Series 201
Convex curve 154
Convex polygon 77
Convex polyhedron 87
Convex quadrilateral 193 (probs. 2 3)
Convex regions 77 154 196 22)
Convexification 154 158 159
coordinates 117
Counter-examples 25—27
cube 88 197 27)
Cube, magic 50
Cylinder 111 (prob. 1)
Deficient number 205 (prob. 9)
Descartes, Rene 15 118
Determinant 199 (probs. 11 12)
Diabolic squares 46
Diagonal 77
Diagonal, broken 46
Diameter 156
Difference of two squares 168 (prob. 8)
Directrix 107 114
Discriminant 135
Divergent sequence 200
Divergent series 201
Divisor 161 181
Divisor, greatest common 168—170
dodecahedron 88
Duerer, Albrecht 50 (prob. 6)
Element of a cone 102
Element of a cylinder 112
ellipse 106 108 110 146 147 194
Eratosthenes 163 (prob. 5)
Erdoes, Paul 197 (probs. 23 24) 205
Euclid 165 166 167
Euler's theorem 81
Euler's Theorem for a polyhedron 86—87
Euler's Theorem on a sphere 84—85
Euler's Theorem on a torus 85—86 89
Euler's theorem, applications of 83—89
Euler's Theorem, proof of 81—83
Euler, Leonhard 15 26 167
Factorial 32 33 67 165
Factorization 161 162 163
Factorization, theorem 169
Fermat's last theorem 175
Fermat, Pierre 26 167
Fibonacci sequence 203—204
Five color theorem 96—98
Fly 144—146 150 151
Focus of a hyperbola 109 113
Focus of a parabola 107 114
Focus of an ellipse 108 111
Four color problem 90—98
Fractions 22 205
Franklin magic square 54—57
Franklin, Benjamin 53
Function notation 19 22
Galois, Everiste 189
Gauss' lemma 199 (prob. 13)
Gauss, Karl 189
General position, lines 73
General position, planes 76 (prob. 6)
Geographical maps 79—101
Geometric mean 67—69
Geometry 192—197
Geometry, analytic 116—120
Geometry, induction in 72—89
Goldbach's conjecture 167 168
Graph of an equation 119
Greatest common divisor 168—170
Grossman, H.D. 197 (prob. 27)
Hadamard, Jacques 189
Hamilton, William 189
Heawood, P.J. 93
High point 122—124
Hyperbola 106 108 109 112
icosahedron 88
Image of a figure 139
Induction 22 28
Inequalities 26 30 58—71
Inequalities for roots 61
Inequalities, arithmetic and geometric means 67—69
Inequalities, Weierstrass 70 (prob. 9)
Infinite series 201 202
INTEGER 160
Isoperimetric problem 153—159
Isoperimetric problem for a box 159 (probs. 5 6)
Kempe, A.B. 93
Leibniz, Gottfried 26 122 202 14)
Lieber, Lillian and Hugh Gray 220
Light ray 140 148
Limit of a sequence 200
lines 188 (prob. 16) 197
Lines in general position 73
Low point 124 125
| Magic constant 41 45 56 3)
Magic cubes 50
Magic squares, definition 40
Magic squares, Franklin 54—57
Magic squares, general formula 47 48
Magnification 155
MAP 80
Map, normal 94
Mathematical induction 22 28
Mathematical induction in geometry 72—89
mathematical symbols 14—19
Mathematics 10
Maximum of a function 122—124
Maximum of a quadratic 137 (prob. 3)
Maximum, relative 126—128
Minimum of a function 125
Minimum of a quadratic 134 136
Minimum, paths 140 143 144—146 150
Minimum, relative 127 128
Mirror image 138
Mobius, Alfred F. 93
Morley's theorem 194 (prob. 7)
Morley, R.K. 205 (prob. 14)
Nasik squares 46
Newton, Isaac 15 122
Normal map 94
Notation 19—22 32
Number theory 160—176 204—206
Numerical value 19
octahedron 88
Order of a vertex 86 87 94
Ordinate 117
Origin 116
Panmagic squares 45
parabola 106 107 113 135 148—150
Parameters 48
Pascal triangle 33—35
Pascal, Blaise 35
Pedal triangle 152 (prob. 10)
Perfect number 167 168 205
Perfect squares 46 167 204 205
permutations 178 181 182
Perpendicular bisectors 190
Planes 184 (prob. 10)
Planes in general position 76 (prob. 6)
Points of intersection 188 (probs. 13—15)
Points on a line 197 (prob. 24)
Poker 183 187
Polygonal path 76
POLYGONS 76—79
Polyhedrons 87—89 (probs. 3 7—9)
Polynomials 197—199
Polynomials, giving primes 167
Postulates 18
Prime numbers 25 162
Prime numbers, Euclid's theorem on 165
Prime numbers, number of 164
Prime numbers, twin 165 166
Progression, arithmetic 31 (prob. 21)
Proper color 92 93
Pythagorean triples 171—174
Q.E.D. 19
Quadrant 117
Quadratic, maximum of 137 (prob. 3)
Quadratic, minimum of 134—136
Quadratic, polynomial 197
Quadrilateral 193 (probs. 2 3) 194 195
Ransom, W.R. 206 (prob. 15)
rectangle 129—132 (probs. 4—7) 188
Rectangular coordinate system 116—118
Regions 72—76 80 159
Regions, convex 77 154 196
Regular solids 88 (prob. 4)
Relative maximum 127
Relative minimum 127
Right circular cone 102—106 110—115
Right circular cylinder 111 (prob. 1)
Rufus, W.C. 205 (prob. 12)
Sector 72
Sequences 200 203 204
Seven color theorem 99
Shortest paths 140 143 150
Simple closed path 77
Sphere, Euler's theorem 84—85
Sphere, tangents to a 103—105
Spheres, tangent 197 (prob. 25)
Spider 144—146 150 151
Square numbers 167 204 205
Square numbers, difference of two 168 (prob. 8)
Star of David 83 (prob. 1)
Steiner, Jakob 153
Stereographic projection 84 85
Subscripts 16
Sums 20—22 23 24 30 31 202
symbols 14—19
Symbols, inventors of 15
Symmetry 107 110 138 139
Tait, Peter G. 93
tangents 103—105 197
Tchebychev, Paul 167
tetrahedron 88 151
Theorem 18
Theory of numbers 160—176
Three dots 20
Torus 85 86 89 100
Torus, map theorem on 98—101
Triangle, isosceles 197 (prob. 23)
Triangle, pedal 152 (prob. 10)
Triangles 184 (prob. 7) 192 194 9)
Triangles, maximal 131 195 11)
Triangles, minimal 143 (prob. 10) 144 195
Trigg, C.W. 197 (prob. 25)
Trigonometry 8 9
Twin primes 165 166
Unbounded figure 143 (prob. 5)
Variable 19
Vertex of a cone 102
Vertex order 86 87 94
Vertices 80
Vinogradov, I.M. 167
Weierstrass inequalities 70 (prob. 9)
Weights 187 (prob. 7)
whole number 160
Word 177
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