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Conway J.H. — The Book of Numbers
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Название: The Book of NumbersАвтор: 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.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1998Количество страниц: 310Добавлена в каталог: 07.12.2008Операции: Положить на полку |
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Irrational numbers 23 Irrational numbers, continued fractions for 186 Irrational numbers, Pythagoras and 257 Jackson, Robert, sequences and 84-85 Japanese, words for powers of ten 16 KepierJ. 51 112 Khayy 68 Klostermark, Bemt 248 Knuth, Donald 15 Knuth, Donald, n 60 Kulik, J P. 130 Laddered exponents 98-100 Lagrange numbers 187-189 Lagrange spectrum 188 Lambert H. 239 Landry, F. 139 Large numbers 59-62 Legendre, Adrienne Marie, logarithmic law of 143-144 146 Lehmer, Derrick Norman 129 130 Lehmer, Dick 170 Leibniz’s formula 242-243 Leonardo of Pisa see Fibonacci numbers Lindemann, Ferdinand 25 191 194 Lindemann, Ferdinand, pi ( 25 239 Linear equations 192 Linfoot, E.H. 224 Liouville, J 239 241 Liouville’s number 239-241 Littlewood, John Edensor 145 Logarithmic law, of Legendre 143-144 Logarithms 248-251 Logarithms, harmony, fractions, and 256-257 Long primes, I 6 Long primes, I, l 169-171 Look and say sequence 208-209 Lowest terms 151 Lucas numbers, ( 112 202-203 Lucas, Edouard 135 Ludolph’s number ( 25 238-239 Lunnon, Fred 87 Machin, John 243 Maclaurin see Euler - Maclaurin sum formula Magicians see Shuffles Markov numbers 187-188 Markov spectrum, I 89 Maseheroni see Euler - Mascheroni number Mediant fraction 152 Meeting point, for set of numbers 76-78 Mersenne numbers 135-136 Mersenne, Marin (Father) 135 Metius, Adrian 239 Metonic cyde 175 Million, use of term 13-16 Mobius number 145 Modulus 30 Moessner’s magic 63-65 Monge, Gaspard, shuffle of 165 Monster simple group 62 Month(s) 175 Month(s), naming of 9-10 Morgan, Augustus de 238 Mountains 99 Mountains, bushes and 103 Mountains, Catalan numbers and 105-106 Mountains, parentheses and 104 Multiples 27 Multiplication of nimbers 294 Multiplication of ordinal numbers 271-276 Multiplication table 30-31 Multiplication table and tetrahedral numbers 46 Multiplication, associative law of 216 Multiplication, by geometry 215 Multiplicative pattern 75 76 Murray J.A.H. 14 Names, of months 9-10 (see also Words) Names, of months, continued fractions and 186 Napier’s number e 25 negative numbers see also Gaussian integers Negative numbers, discriminants and 224-226 Negative numbers, square roots of 211-213 Negative remainders 219 Negative, of Hackenbush game 286 Net see Internet Neugebauer, Otto 173 Neusis constructions 195 Neutral Hackenbush 291-292 297 298 Newton, Isaac 226 Newton’s formula, sequences and 81-83 Nexus numbers 53-54 55 Nim, game of 291-298 Nimbers, and game of Nim 291-298 Nineteen, word for 11 Ninety, word for 12 Nonprime, shuffles and 168 Norm 232 Notation, arrow 60 (see also Number system) Notation, place 17 Number families 91-126 Number families, Bell numbers 91-93 Number families, Bernoulli numbers 107-109 Number families, Catalan numbers 101 Number families, Euler numbers and zigzag arrangements 110-111 Number families, Faulhaber’s formula 106 Number families, Fibonacci numbers 111-113 Number families, laddered exponents 98-100 Number families, partition numbers and compositions 94-98 Number families, phyllotaxis 113-121 Number families, Stirling set numbers 92-94 Number sequences 63 Number system, bases of 21 Number system, Egyptian 18 19-20 Number system, Greek 18 Number system, Hindu - Arabic 18 20-21 Number system, Roman 19 Number system, Seleucid 18 Number walls 85-87 Number walls, windows in 87-89 Number(s) see also Irrational numbers; Rational numbers Number(s), algebraic 23 181-210 Number(s), arrangement 66 Number(s), cardinal 25 277-279 Number(s), centred square 41 42 Number(s), complex 23 Number(s), composite 127 Number(s), even 27 Number(s), factorial 64 65-66 Number(s), golden 184 Number(s), hex 41 Number(s), hexagonal 39 Number(s), hypercomplex 230-232 Number(s), imaginary 211-214 Number(s), infinite 25 Number(s), infinite and infinitesimal 265-299 Number(s), irrational 23 Number(s), Lagrange 187-189 Number(s), Markov 187-188 Number(s), nexus 53-54 55 Number(s), octahedral 50-52 53 Number(s), odd 27 Number(s), online, internet-based checker 26 Number(s), ordinal 25 266-276 Number(s), pentagonal 39 Number(s), pentatope 55-57 70 Number(s), polygonal 38-42 Number(s), prime 127-149 Number(s), pronic 34 Number(s), rational 23 Number(s), rhombic dodecahedral 53-54 Number(s), root of word 1 Number(s), samples of favorite 24 Number(s), singly even 30 Number(s), square 30-33 Number(s), square pyramid 47-49 Number(s), surreal 25 283-284 Number(s), tetrahedral 44-46 70 Number(s), transcendental 23-25 237-263 Number(s), triangular 33-38 39 70 Number(s), use of word 1 Number(s), very large 59-62 Number(s), whole 22 Number(s), word systems for 2-16 Number(s), writing of 17-22 Numbers modulo 130 Numerals 17-22 Numerator 151 Octahedral numbers 50-52 53 Octahedral numbers, truncated 52 Octal system 21 Octave 256-257 Octonions 234 Odd numbers 27 Odd numbers, tetrahedral 46 One hundred and sixty-three, importance of 25 One-to-one correspondence 277 Online resource, number checker as 26 Orders 66 Ordinal numbers 25 Ordinal numbers, Cantor’s 266-271 275-276 Ordinal numbers, multiplying 271-276 Out shuffle 163 164 165 Pacioli, Luca (Fra) 184 Parabolas 32 Parentheses 100 Parentheses and shaking hands 104 Partial quotients 178 Partition numbers and compositions 94-98 Pascal, Blaise 68 Pascal’s triangle 63 67 68-70 94 Pascal’s triangle, Catalan numbers and 101 Pascal’s triangle, coefficients and 72 73 Patterns, arrangement numbers 66 Patterns, choice numbers 67-68 Patterns, choice numbers as binomial Patterns, coefficients 72-74 Patterns, choice numbers with repetitions 70 Patterns, colors and 29-30 Patterns, factorial numbers 65-66 Patterns, frieze 74-76 Patterns, guessing next term in sequence 79-89 Patterns, Moessner’s magic 63-65 Patterns, number of regions 76-79 Patterns, Pascal’s triangle 63 67 68-70 Pell equation 204 Pentagon, folding 185 Pentagonal numbers 39 96-97 Pentatope numbers 55-57 70 Periodic points 207-209 permutations 66 Phyllotaxis 113-121 Physics, geometry of 213 Pi ( 25 194 Pi ( 237-239 Pitch 257 Place notation 17-18 Planck length 213 Plants, bud arrangement and 122-124 Plants, phyllotaxis and 113-121 Platonic solids 53 Plimpton 322 17 174 176 Plouffe, Simon 25 Poker hands 70-71 Pollard, John 139 Polygon(s), and trees 103 Polygon(s), as triangles 97-98 Polygon(s), Catalan numbers and 101-102 Polygon(s), constructing regular 197-202 Polygon(s), seventeen-sided 25 Polygonal numbers 38-42 Polygonal numbers, building 42 Polynomials, of degree two 32 Powers of 251-254 Powers of 16 Primality, Wilson’s test for 220 Prime denominator 161 Prime numbers 127-149 Prime numbers, arithmetic modulo 130-132 Prime numbers, defined 127 Prime numbers, discriminants and 224-226 Prime numbers, Fermat 137-141 Prime numbers, Fermat’s test for 141 143 Prime numbers, fractions 147-148 Prime numbers, frequency of 143-145 Prime numbers, guesses and 145-146 Prime numbers, Mersenne’s 135-136 Prime numbers, news 133-135 Prime numbers, prime factors and 132-133 Prime numbers, sum of two squares 146-147 Primes, Gaussian 218 219 Primes, integers and 223 Primes, long 169-171 Primitive 227 Projections 42 Pronic number 34 Pyramid numbers, square 47-49 Pyramids, hex 43 Pythagoras 23 213 Pythagoras, fractions and 152 Pythagoras, geometric problems and 182 Pythagoras, number ( 25 Pythagoras, Theorem of 182-183 192 Pythagorean fractions 171-173 256 257 Pythagorean fractions, Babylonian table of 173 174 Pythagorean triples 173 Pythagorean triples, “Quad-,” “quar-,” “quat-” words 8 11 Quadratic equations 192 211 Quadratic expressions 32 Quadratic residues 31 Quadratic surds 190 Quaternions 231-232 Quaternions, machine for 232-234 Quotient-difference table 86-87 Quotients, partial 178 Rademacher, H. 95 Ramanujan numbers 96 Ramanujan, Srinivasa 95 Ratio, golden number and 184 Rational numbers 23 151 183 Rational triangle 228 Ratios 183 Ratios, harmony, fractions, and 256-257 Regions, patterns and 76-79 Regular polygon, constructing 197-202 Regular solids 53 Remainder 28 Residue classes 28 Residue(s), colors, patterns, and 29-30 Residue(s), quadratic 31 Rhind papyrus 23 237 Rhombic dodecahedral numbers 53-54 Riemann hypothesis 145 Riemann, Georg Friedrich Bernhard 145 146 Rodrigues 234 Roman number system 19 Roman number system, fractions in 22 23 Rooted plane bushes 99 Rulers, Euclid and 191-192 Scalar pan 231 Secand numbers 110-111 Seleucid number system 18 Semiregular solids 53 Sequences see also Patterns; Shuffles
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