Авторизация
Поиск по указателям
Conway J.H. — The Book of Numbers
Обсудите книгу на научном форуме
Нашли опечатку? Выделите ее мышкой и нажмите Ctrl+Enter
Название: The Book of Numbers
Автор: Conway J.H.
Аннотация: In this book, John Horton Conway, creator of the famous game of Life, and one of the most original thinkers in mathematics, joins up with Richard K. Guy, whose broad understanding of the subject is often dressed up in playful expository language. Together they lead the reader on an imaginative, often astonishing tour of the landscape of numbers.
The Book of Numbers is just that-an engagingly written, heavily illustrated introduction to the fascinating, sometimes surprising properties of numbers and number patterns. The book opens up a world of topics, theories, and applications, exploring intriguing aspects of real numbers, systems, arrays and sequences, and much more. Readers will be able to use figures to figure out figures (do arithmetic and algebra by geometry), rub elbows with famous families of numbers, prove the primacy of primes, fathom the fruitfulness of fractions, imagine imaginary numbers, investigate the infinite and infinitesimal, and more...
Conway and Guy, who are co-authors (with E.R. Berlekamp) of Winning Ways For Your Mathematical Plays, combine their unusual talents to present readers with mathematical topics that are infused with their unique perspectives, little-known numbers, clever insights, and historical curiosities. For math buffs looking to explore new twists and turns in number theory, The Book of Numbers promises to be a richly rewarding reading experience.
John Horton Conway is Professor of Mathematics at Princeton University. Among his many publications and books are Winning Ways For Your Mathematical Plays (with E.R. Berlekamp and Richard Guy), On Numbers and Games, and Sphere Packing, Lattices, and Groups (with N.G.A. Sloane).
Richard K. Guy is Professor Emeritus in the Department of Mathematics at the University of Calgary, Alberta. With more than 200 publications and ten books published, Guy is universally known for his work with unsolved problems and number theory.
Язык:
Рубрика: Математика /
Статус предметного указателя: Готов указатель с номерами страниц
ed2k: ed2k stats
Год издания: 1998
Количество страниц: 310
Добавлена в каталог: 07.12.2008
Операции: Положить на полку |
Скопировать ссылку для форума | Скопировать ID
Предметный указатель
factorial 65
th Bell number 93
th harmonic number 258-259
see Arithmetic modulo
Ackermann numbers 60
Adams,J. F. 235
Addition of nimbers 293
Addition, associative law of 216
Addition, by geometry 215
Addition, in Hackenbush game 287
Additive pattern 74
Aleph zero ( ) 25 278
Algebra, geometry and 27-62
Algebra, shuffles and 167
Algebraic equations 194
Algebraic equations for girls and boys 205-206
Algebraic numbers 23 189-190
Algebraic numbers of degree three 190-191
Algebraic numbers of degree two 190
Algebraic numbers, geometry and 181-210
Algebraic numbers, in arithmetic problems 202-205
Angle(s) 195-197
Angle(s), bisectors of 199 202
Angle(s), neusis trisection of 195
Angle(s), trisectors of 198-199
Apery’s number 261-262
Arabic number system 18
Arabic number system, 20-21
Archimedean solids 53
Archimedes and pi ( ) 238
Archimedes, neusis trisection of angle 195
Arithmetic, geometry and 27-62
Arithmetic, geometry and, modulo 130-132
Arithmetic, geometry and, problems, algebraic numbers in 202-205
Arithmetic, geometry and, progression 35-38
Arrangement numbers 66
arrow notation 60
Artin, Emil 170
Associative law of addition 216
Associative law of addition of multiplication 216
Astronomy 17-18 175
Axiom of Choice 274-275
Axis 199
Babylonian cuneiform 173-174 181-182
Babylonian cuneiform, numerals 17 20-21
Baker, Alan 224
Bases, numbers in 21
Bell numbers 91-93
Bell, Eric Temple 91
Berlekamp, Elwyn 288
Bernoulli numbers 107-109
Bernoulli, Jacob (James) 107
Bifurcating trees 98
Bifurcation points 208
Billion, use of term 13-16
Binary numbers 21
Binary trees 98
Binary trees, exponentiations and 103
Binomial theorem 43 73
Bisectors 199 202
Bouton, C.L. 291
Brent, Richard 139
Brillhart, John 139
Brown, J. 136
Buds see Phyllotaxis Bushes
Buds, exponentials and 103
Buds, mountains and 104
Calabi, Eugenio 206
Calabi’s triangle 206
calendar 175
Cantor, Georg 25 (see also Cardinal numbers; Ordinal numbers)
Cantor, Georg and aleph zero ( ) 25
Cantor, Georg and cardinal numbers 25
Cantor, Georg, counting cards and 279-282
Cantor, Georg, infinite numbers and 25
Cantor, Georg, ordinal numbers of 25 266-271 275-276
Cardinal numbers 25 277-279
Cardinal numbers, counting cards and 279-282
Cardinal numbers, first infinite ( ) 278
cards see Shuffles
Carmichael numbers 142
Casting out the nines 28-29
Catalan numbers 101
Catalan numbers, mountains and 105-106
Cayley numbers 234-235
Cayley, Arthur 234
Centred cube numbers 52
Centred square numbers 41 42
Chain, Hackenbush 286 287 289
Choice numbers 67-68
Choice numbers with repetitions 70
Choice numbers, as binomial coefficients 72-74
Chuquet, N. 13 14
Circle, degrees of 17
Circle, squaring of 191
Classes, ordinal and cardinal numbers in 277-278
Clausen 109
Coefficients 72
Cohen, Paul 282
Colors, patterns and 29-30
Combinations 67
Comma of Pythagoras 257
Compass, Euclid and 191-192
complex numbers 23 214
Composite numbers 127
Compositions 95
Computers, very large numbers and 59-60
Congruence, “casting out the nines” and 28-29
Congruent modulo 28
Congruent to 1
Congruent to, modulo 3 28
Constructions, of Euclid 191-192
Continued fractions 175-179
Continued fractions, harmony, logarithms, and 257
Continuum Hypothesis 282
Convergents 178
Countable set 278-279
Counting 275-276 (see also Ordinal numbers of same set in different ways)
Counting cards 279-282
Counting numbers 69
Counting, from zero 265-266
Cube numbers, centred 52
Cubes 42
Cubes, Sums of 57-58
Cubes, tesseracts as 55
Cubes, very large numbers and 59
Cuneiform script 17 173 174 181-182
Cycle, Metonic 175
De divina proportione (Pacioli) 184
De la Roche, Emile 14
De la Vall e Poussin, Ch. - J. 260
De Moivre numbers 227 228
De Moivre numbers, circle cutting 226-228
De Moivre numbers, seventeenth-order 229
De Moivre, Abraham 226
Decimal system 21
Decimals, fractions and 157-163
Degree(s) algebraic numbers and 189
Degree(s) algebraic numbers and of circle 17
Delian number ( 193-194
Denominator 151
Denominator of fractions 157-160
Diaconis, Persi 165
Difference table 80 (see also Patterns;Sequences)
Differencing, sequences and 79-81
Dimensions fourth 55-59
Dimensions fourth, third 42-44
Diogenes 255
Diophantus of Alexandria 172
Dirichlet, G.I. 260
Distance 3 296 297
Division, by geometry 215
Dubois - Raymond, Paul 299
Dubois - Raymond, Paul, , powers of 251 254
Egyptian number system 18 19-20
Eighty, words for 12
Eisenstein integers & units 205 220-221 222 223
Elements of Geometry, The (Euclid) 132
Empty set 266
Equations, algebraic 194
Equations, linear 192
Equations, Pell 204
Equations, quadratic 192
Equilateral triangle 206
Eratosthenes 127-128
Euclid, Mersenne primes and 137
Euclid, number theory and 132-133
Euclid, perfect numbers and 139
Euclid, ruler and compass constructions 191-192
Euclidean numbers 192-193
Euler - Maclaurin sum formula 260-261
Euler - Mascheroni number 17 25 260
Euler numbers 110-111
Euler, Leonard 137
Euler, Leonard, prime numbers and 225
Euler, Leonard, torient numbers of 154-156 167 198
Euler, Leonard, transcendental numbers and 253 254-256
Eulerian number, 111
Euler’s formula, for partition numbers 95
Even numbers 27
Exponentials, bushes and 103
Exponentiations, trees and 103
Exponents, laddered 98-100
Factor Table for the First Ten Million (Lehmer) 129-130
Factorial 65
Factorial numbers 64 65-66
Factors, prime 132-133
Families, of numbers 91 126
Farey series 152-154 156
Faulhaber’s formula 106 (see also Bernoulli numbers)
Faulliaber, Johann 106
Fermat numbers 137-141
Fermat, Pierre de 138
Fermat, Pierre de, Little Theorem of 09 164
Fermat, Pierre de, prime numbers and 220
Fermat, Pierre de, prime of 197
Fermat, Pierre de, sum of two squares theorem 221
Fermat, Pierre de, test for primes 141-143
Fibonacci numbers 85 111-113 202-203
Fifth (interval) 256
Finite set 278
flowers see Phyllotaxis
Ford, Lester R., Farey series and 153-154
Ford, Lester R., “Four,” use of word 8
Four-square formula 232
Fourth dimension 55-59
Fractions 23 151-179
Fractions and gear trains 178 179
Fractions for irrational numbers 186
Fractions modulo p 130-132
Fractions, as rational numbers 151 183
Fractions, babylonian table of Pythagorean 173 174
Fractions, continued 175-179
Fractions, decimals and 157-163
Fractions, harmony, logarithms, and 256-257
Fractions, long primes and 169-171
Fractions, prime numbers and 147-148
Fractions, Pythagorean 171-173
Fractions, Roman 22 23
Fractions, shuffling and 163-168
Fractions, Wilson’s theorem and 168-169
Freiman, G. A. 188
Freiman’s number 188
Frequency, of prime numbers 143
Frieze patterns 74-76 96-97
Frieze patterns, polygons and 101
Games, Hackenbush 284-291 (see also Green Hackenbush; Neutral Hackenbush)
Games, Nim 291-298
Gardner, Martin 41 225-226
Gauss, Carl Friedrich 11 28
Gauss, prime and 139-140 144 146
Gauss, regular polygon and 193
Gaussian integers 217-223
Gauss’s numbers 244-245
Gear trains, fractions and 178 179
Generalized Continuum Hypothesis 282
Geometry and algebraic numbers 181-210
Geometry of physics 213
Geometry, adding and multiplying by 215
Geometry, arithmetic and algebra figured with 27-62
Geometry, polygons and 198-202
Gnomon 32 42
Gnomon and sums of cubes 57-58
Gnomon, bending nexus numbers and 55
Gnomon, defined 33
Godel, Kurt 282
Golden number (t) 25 112 123 184
Golden rectangle 184
Golden rule, for fractions 151
Graham, Ron, hexagon of 206-207
Graham’s number 61-62
Greece, algebraic numbers and 190-191
Greek number system 18
Green Hackenbush 297
Gregory numbers 241-243 244-245 246 247
Gregory, David 242
Hackenbush game 284-291
Hackenbush game, Green Hackenbush 297
Hackenbush game, Neutral Hackenbush 291-292 297 298
Hadamard, Jacques 143-144
Hamilton, William Rowan 231 234
Handshakes without crossing 100
Handshakes without crossing, parentheses and 104
Hardy G.H. 95
Harmonic numbers 143 258-259
Harmony, fractions, logarithms, and 256-257
Harmony, fractions, logarithms, and, words 12-13
Heegner 224 225
Heilbronn, H.A. 224
Heptadecagon 229-230
Hex numbers 41
Hex pyramids, as cubes 43
Hexadecimal system 21
Hexagon, folding 185
Hexagon, Graham’s 206-207
Hexagonal number 39
Hindu - Arabic number system 18 20-21
Hundred, words for 12-13
Hurwitz, A. 235
Hypercomplex numbers 230-232
imaginary numbers 211-214
In shuffle 163 164
Incommensurable numbers 213
Infinite and infinitesimal numbers 25 265-299
Infinite and infinitesimal numbers, Cantor’s ordinal numbers 266-271 275-276
Infinite and infinitesimal numbers, counting cards and 279-282
Infinite and infinitesimal numbers, Hackenbush game and 284-291
Infinite and infinitesimal numbers, multiplying ordinal numbers 271-276
Infinite and infinitesimal numbers, nimbers and game of Nim 291-298
Infinite and infinitesimal numbers, orders of infinity 299
Infinite and infinitesimal numbers, Sierpi ski and 265-266
Infinite and infinitesimal numbers, surreal numbers and 283-284
Infinitesimal numbers see Infinite and infinitesimal numbers
Infinity, orders of 299
Information sources, on number sequences 89
Integers, gaussian 217-223
Integers, unique factorization into primes 223
Integral lexicographic code 296
Internet, number checker on 26
Inverse Symbolic Calculator 25 26
Реклама