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| Penney D.E. — Perspectives in Mathematics |
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| Предметный указатель |
Absolute value 289
Aleksandrov, A.D. 318
Alexandroff, Paul 317
American Mathematical Monthly 107
Antoine, L. 51
Approximations by continued fractions 63—65
Archimedean property 303
Area 21
Art Gallery Theorem 254
Associative law 82
Associative operations in real number system 301
Bach, J.S. 52 76
Banach, S. 21—23
Batting average 66
Beck, Anatole 318
Beet virus molecule 142
Beiler, A.H. 218 316
Benade, Arthur H. 81
Benson, R.V. 279
Bers, Lipman 317
Birkhoff, Garrett 106 316
Bleicher, Michael N. 318
Boltyanskii, V.G. 23 279
Bolyai Farkas 23—24
Bolyai Farkas, Janos 24
Bolyai — Gerwin Theorem 2 6
Borromean rings 25 see
Borromean Rings, formula 41
Borromean Rings, generalizations 29
Brunn, H. 29 51
Brunnian links 29
Brunnian links, (4,2)-links 45—46
Brunnian links, (n,k)-links 43 49
Cancellative operations 95
Cantor ternary set 312
Cantor Ternary Set, length 313
Cantor Ternary Set, number of elements 314
Cantor — Schroeder — Bernstein Theorem 164
Cantor — Schroeder — Bernstein Theorem, applications 169—172 176 181
Cantor, Georg 177 182
Cardinal numbers 179
Cardinal numbers, existence 180
Center of group 104
Cohen, Paul J. 182
Cohn-Vossen, S. 143 317
Commutative law 34
Commutative operation in group 87 94 see Abelian"
Commutator 45
Commutator, k-commutator 48
Complex number system 310
Composite numbers 185
Composite numbers, consecutive 187
Composite numbers, prime factors 186
Congruence motions of disk 90
Congruence motions of square 93
Congruence motions of tetrahedron 90
Congruence motions of triangle 83—87
Congruence motions, product 84—85
Constructions with straightedge and compass 6 19 23
Continued fractions 59—61
Continued fractions and batting averages 66—67
Continued fractions and grade distributions 67—69
Continued fractions and irrational numbers 286
Continued fractions, construction 75—76
Continued fractions, evaluation 62—63
Continuum 179
Convex hull 261
Convex hull, kernel 261
Convex hull, polyhedron in Steinitz's Theorem 116
Convex hull, sets, intersection of 258—260
Convex hull, sets, tower of 260
Convexity 255
Convexity, generalizations 276—279
Coset of subgroup 96
Coxeter, H.S.M. 143 317
Critical point 240
Cross-cancellative operation 95
Cross-cancellative operation, semigroup 105
Crowdis, David G. 318
Crowe, Donald W. 318
Crowell, R.H. 51
Curve, knotted 30
Curve, knotted on torus 30
Curve, knotted, polygonal 28
Curve, knotted, simple closed 27—30
Curve, knotted, tame 28
Curve, knotted, wild 28
Cycles in population 249
de Fermat, Pierre 184
Debrunner, H. 23 51 279 317
Decimal expansion 308—309
Dedekind Box Principle 172 175
Dedekind Box Principle, applications 177
Dedekind infinite 174
Dedekind, Richard 183
Degree of realization 230 232
Degree of realization in competing populations 234
Dehn, M. 18
Differential equations 223
Differential equations for competing populations 234 245
Differential equations in population growth 224—226
Differential equations in radioactive decay 227
Divisibility 184
divisors 184 see
Divisors, number 205
Divisors, product 189
Doerrie, Heinrich 317
Dudley, Underwood 218
Duplication of cube 18
Dynkin, E.B. 143
Equidecomposable figures 3 22 23
Equivalence relation 5 162
Equivalence relation, between nested sequences 293 295
Euclidean algorithm 92 196 197 219
Euclidean algorithm, proof 197—202
Euler's formula 108 118
Euler's formula, proof 118—122
Euler, L. 118 144
Exponent of group element 98
Factorization into primes 196 202 209—210
Fermat's theorem 218
Fifths 73
Fifths, improving 77
Five-color theorem 144
Fort, M.K. 51
Fox, R.H. 51
Fraleigh, John B. 318
frequencies 70
Frequencies of notes on piano 73
Functions 154—162
Fundamental Theorem of Arithmetic 202 204
Fundamental Theorem of Arithmetic, applications 281
Fundamental Theorem of Arithmetic, proof 202—203
Gause, G.F. 252
Gauss, C.F. 218—219
Gelfond, A. 218
Generator of group 102
Geodesic dome 142
Geometric series 283
Goffman, Caspar 315
Golden mean 62
Greatest common divisor 205
Greatest common divisor, computation 205—206
Greek alphabet 319
Griffin, Harriett 218
Group 92
Group of prime order 102
Group, abelian 102
Group, associated with curves in space 38
Group, center 104
| Group, cyclic 102
Group, examples 82—92
Group, uniqueness of identity 93
Gruenbaum, Branko 143 279
Hadwiger, H. 18 23 279 317
Half-plane 273 275
Hall, M. 106
Harmonics 70
Hausdorff, Felix 182
Helly's theorem 266 268
Helly's Theorem, applications 270—271 273 276
Herstein, I.N. 106
Hilbert, D. 143 317
Hocking, John G. 317
Homomorphism 105
Horn, Alfred 279
Image of function 155—156
Image of homomorphism 105
Induction principle 10 190
Induction Principle and well-ordering 190—193
Induction Principle, applications 10—11 49 193—195 259
Infinite series 69—70 295
Integers 184
Intermediate fractions 64
Intervals 288
Intervals, length 288
Intervals, nested sequences of 293
Intervals, sum of 297
Inverse of group element 83
Inverse of group element, uniqueness of 93
Jacobson, Nathan 106
Jakobson, Roman 317
Jeans, Sir James 81
Join of point and set 277
Kernel of homomorphism 106 see
Khinchine, A.Ya. 81
Klee, Victor 23 279 317
Kolmogorov, A.N. 318
Krasnoselskii's Theorem 254 271
Krasnoselskii, M.A. 271
Kripke, Bernard 315
Kurosh, A.G. 106
L-convexity 277
Lack, D.L. 253
Lagrange's theorem 96
Lagrange, J.L. 107
Lavrent'ev, M.A. 318
Law of quadratic reciprocity 218
Law of Small Whole Numbers 72
Least upper bound 303
Limit of sequence 65 69 284 289—291 294—295
links 30 32 see
Links, splittable 30
Lobachevsky, N.I. 24
Logarithms 53—56
Lomont, J.S. 317
Lyusternik, L.A. 143 279
MacLane, Saunders 106 316
Mansfield, M.J. 314
Map on Moebius strip 117
Map on sphere 116
Map on torus 116
Moebius strip 50 117
Moise, E.E. 23
Mordell, L. 218
n-link 30
n-link, completely splittable 32
n-link, splittable 30
n-link, sublink of 32
Natural numbers 184
Natural numbers, composite 185
Natural numbers, prime 185
Nested sequences of intervals 293
Nested sequences of intervals, equivalence of 295
Net of polyhedron 118
Niven, Ivan 218 316
Nonmeasurable set 21
Odum, Eugene 253
One-to-one correspondence 156 160—162
Order of group 96
Order of group of group element 99
Order of group, infinite 96 99
Ordered pair 159
Ore, Oystein 143
Parallelogram formed from triangle 11
Parallelogram formed from triangle, reassembled into rectangle 11
Partial quotients 62
Passman, D.S. 106
Polya, George 192 318
Polygon 2 109
Polygon, connected 109
Polygon, edge 2
Polygon, equidecomposable 3
Polygon, vertex 2
Polyhedron 113
Polyhedron, 2-connected 116
Polyhedron, edge 115
Polyhedron, face 115
Polyhedron, vertex 115
PRIMES 102 185
Pythagorean right triangles 217—218
Pythagorean Theorem 16
Rademacher, Hans 218
Radioactive decay 227
Rational numbers 280
Real numbers 297
Real numbers as nondenumerable set 178
Real numbers, Archimedean property 303
Real numbers, decimal expansions 308—309
Real numbers, order relation 302
Rectangle formed from parallelogram 11
Rectangle formed from parallelogram, reassembled into square 12—14
Regular solid 123
Rudin, Walter 314
Schoenflies theorem 110
Semigroup 104
Sets 146
Sets and Venn diagrams 151
Sets, algebra 153
Sets, cartesian product 160
Sets, convex 255
Sets, denumerable 176
Sets, descriptive definition 147
Sets, difference 154
Sets, distributive laws 152—153
Sets, element 146
Sets, empty 150
Sets, equality 148
Sets, finite 163
Sets, inclusion 149
Sets, infinite 163
Sets, intersection 150
Sets, listing 147
Sets, maximal convex 264
Sets, maximal tower 263—264
Sets, maximal with respect to a property 263
Sets, nondenumerable 177
Sets, nonlinear 263
Sets, notation 147—148
Sets, number of elements 154
Sets, subset 149
Sets, tower 260
Sets, union 149
Sierpinski, W. 23
Sigmoid curve 232
Singer, I.M. 51
Slobodkin, Lawrence B. 253
Snowflake curve 19—21
Spivak, Michael 317
Sprecher, David A. 315
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