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Conway J.H. — The Book of Numbers
Conway J.H. — The Book of Numbers

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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: en

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
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Предметный указатель
$n$ factorial      65
$n$th Bell number      93
$n$th harmonic number      258-259
$p$      see Arithmetic modulo $p$
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 ($\aleph_{0}$)      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 ($\pi$)      238
Archimedes, neusis trisection of angle      195
Arithmetic, geometry and      27-62
Arithmetic, geometry and, modulo $p$      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 ($\aleph_{0}$)      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 ($\aleph_{0}$)      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$\acute{e}$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 ($\sqrt[3]{2})$      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, $e$, 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, $A (n, k)$      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 $n$      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$\acute{n}$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
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