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Higgins P. — Mathematics for the curious
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Название: Mathematics for the curiousАвтор: Higgins P. Аннотация: When do the hands of a clock coincide? How likely is it that two children in the same class will share a birthday? How do we calculate the volume of a doughnut? Mathematics for the Curious provides anyone interested in mathematics with a simple and entertaining account of what it can do.
Author Peter Higgins gives clear explanations of the more mysterious features of childhood mathematics as well as novelties and connections that prove that mathematics can be enjoyable and full of surprises. Topics include: the truth about fractions, the questions and their answers, and the golden ratio. Higgins poses entertaining puzzles and questions tempting the reader to ponder math problems with imagination instead of dread. Mathematics for the Curious is an accessible introduction to basic mathematics for beginning students and a lively refresher for adults.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1998Количество страниц: 224Добавлена в каталог: 16.12.2013Операции: Положить на полку |
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Achilles and Tortoise 8 Algebraic semigroups 219 Algorithm 80 203 Algorithm euclidean 78 80—84 181—182 Alphabet 217 Angle at the centre 68 Angle at the circumference 68 Angle in a semicircle 66 Angle, corresponding 56 Angle, reflex 69 Angle, right 39 54 Angle, straight 56 Angle, supplementary 72 Anti-logarithm 44 Ascent of Man 175 Associative law 95 Automaton 217—220 Automaton, language of 217 Average 15 Base 11 BASEBALL 15 170 Bertrand — Whitworth Ballot Problem 168—169 BINARY 11 Binomial coefficient 89 109 164 Binomial number 89 Binomial theorem 110 157 Birthday problem 158—161 Bluffing 174 Brahe, Tycho 45 Bronowski, J. 175 Buffon's Needle Problem 122 Calculators 24 Cantor, Georg 52 Carry 97 Characteristic 44 Chessboard 120 123 147—148 circle 64 Circle theorems 54 64—72 188 Circle, area of 61 Circle, circumference of 18 61 Circle, through three points 71 Circuit 202 Clock problems 6—9 Collinear 68 71 Common difference 88 143 Common ratio 139 Commutative law 96—97 101 Compasses and straight edge 39 66—67 Completing the square 102—104 106 173 components 200 Compound interest 155—157 Compound interest, Bernoulli's Problem of 156 Computers 24 Concatenation 193 Concurrent lines 71 conjugate 180 Convergents 184 Convex 213 Cricket 15 Cross-multiplication 27 Data, the android 174 De Divina Proportione 187 Decibel scale 45 Decimals 32—38 Decimals, recurring 33 Decimals, terminating 33 Delian problem 51 Denominator 27 Denominator, common 28 79 106 Denominator, rationalizing the 180 Descartes, Rene 72 Diagonal argument 52—53 Difference of two squares 109 Discontinuity 69 Distributive law 94—99 dodecahedron 198—199 Doudecimal 11 Doughnut 133—135 Edges 200 Ethiopean traders 94 98—99 Euclid's lemma 77 83 Euler — Mascheroni constant 151 Euler, Leonhard 77 87 100 128 141 Face 210 Face number 212 Factorial 87 92—93 167 Farey series 25 Fermat's last theorem 84—86 Fermat's principle of least time 131—132 Fermat, Pierre de 85—86 Fibonacci's Rabbit Problem 190—193 Foot 13 Fractions, continued 181—185 Fractions, Egyptian 31 110—112 152—153 Fractions, improper 33 Fractions, proper 31—32 Fractions, reduced 27 Fractions, unit 31 110—112 Fractions, vulgar 32 Galileo, Galilei 47 Game theory 173—179 Gardner, Martin 22 Geometry 38 54—75 Geometry, analytical 72 Geometry, Euclidean 54 72 Goldbach conjecture 84 Golden Quadratic 192 Golden ratio 70 185—199 Golden rectangle 186—187 Golden section 188—190 Graph theory 203 Hand-shaking Lemma 201 Herodotus 58 Heron of Alexandria 129 Heron Problem 129—132 165 hexagons 63—64 Highest common factor 29 78 79—82 Hypotenuse 39 Icosohedron 198—199 Imperial system 12 InCh 13 Inclusion-Exclusion Principle 141 Inductive argument 20 Input 217 Integers 47 Interleaving 48 Interpolation 45 Isthmus 203 Kepler, Johann 45 Kilogram 12 Koenigsberg bridges problem 128 200 Kuratowski, K. 205 Lagrange, J.L. 187 Lattice path 166—168 Laws of indices 42—43 LIMIT 139 Lindemann, C. 51 Line(s), equation of 72 Line(s), parallel 56 Logarithms 43—46 104 Logarithms, laws of 44 104 Logarithms, natural 45 88 137 140 151 157 Loops 200 Lunes 58—59 Mails Slot Principle 124 Mantissa 44 Mathematical Puzzles and Diversions 22 Mathematics and its History 197 Mean, arithmetic 104 Mean, geometric 104 Mental arithmetic 99 Metre 13 Metric system 12 Monty Hall problem 116—118 Morra 175—177 MrSpock 174 177 Multi-edges 200 Napier, John 45 National Lottery 87 113—115 158 Network(s) 127 201—220 Network(s), complement of 206—208 Network(s), complete 205 Network(s), isomorphic 208 Network(s), monochromatic 215 217 Network(s), planar 200 204—214 Network(s), plane 209 Network(s), simple 205 Network(s), traversing of 201 Newton, Isaac 161 nodes 200 Nodes, adjacent 208 Nodes, degree of 201 Nodes, even 200—201 Nodes, odd 200—201 Number(s), abundant 76 Number(s), algebraic 50 see Number(s), Bernoulli 147 Number(s), composite 77 Number(s), constructible 39 Number(s), coprime 83 Number(s), Fibonacci 190—195 Number(s), irrational 38 Number(s), Mersenne 88—89 Number(s), mixed 33 152 Number(s), natural 47 Number(s), negative 107—108 Number(s), perfect 76 Number(s), prime 35 77 142 Number(s), random 176 Number(s), rational 33 see Number(s), real 38 see Number(s), transcendental 51 see Numerator 27 octahedron 196 One-to-one correspondence 4 123 208 Pacioli, Luca 187 197 Palindromes 219—220 Paper, Stone, and Scissors 175 Parallelogram 60 74 Parallelogram, area of 60 Pascal's triangle 90—93 109 Pence 26 Penrose, Roger 65 Pentagon 188—190 195 207 Percent 10—14 Perpendicular bisector 66 71 pH scale 45 Pigeon-hole principle 124 159 220 Poker 164 174 Polygon, inscribed 62 Polygon, regular 61 Polyhedra 213 Polyhedral formula 212—214 Polyhedron 196 Polyhedron, dual 196 Polyhedron, regular 195 Pounds 26 Power 2 PRIMES 35 see Primes, factorization 77 Primes, formulae for 86—87 Primes, infinity of 79 Primes, Mersenne 77 88 Prisoners' dilemma 178—179 probability 158—172 Probability, conditional 116 Probability, geometric 122 PRODUCT 26 Product, infinite 155—156 Product, Viete 156 Product, Wallis 155 185 Pythagoras's theorem 1 17 54—59 133 197—198 Pythagorean triples 84—86 Pythagoreans 38 Quadratic 87 Quadratic, equation 102—104 Quadratic, formula 106 185 Quadrilateral 63 74 Quadrilateral, concyclic 70—71 Quilters 65 Quotient 26 Radian 62 Ramsey's theorem 127 214—217 Ramsey, F.P. 127 Reciprocal 30 110—111 180 Rectangular coordinates 72 Recursion 22 191 Regular solids 195—199 Renaissance 107 195 Rewriting rules 194 Richter scale 45 Roulette 169—170 Russell, Bertrand 100 Russian roulette 119 150 Samuel Pepys's Problem 161—163 Sector 68 Self-duality 196 Semicircle 58 66 Sequences of squares 144 Sequences, arithmetic 142—143 Sequences, geometric 147 191—192 Sequences, papal 193—195 Series, arithmetic 18 Series, finite 142—149 Series, Fourier 140 Series, geometric 2 120 142 147—151 157 169 215 Series, harmonic 138—139 151—153 Series, infinite 149—155 Series, telescoping 144 148 154 Set of algebraic numbers 50 Set of integers 47 Set of reals 53 Set of transcendentals 53 Set, countable 52 Set, ofrationals 48 Set, uncountable 24 52 Shillings 26 Snell's law 132 Square roots 38 101—102 104—106 Squaring the circle 51 Star Trek 173 States (of an automaton) 217 States (of an automaton), accepting 217 States (of an automaton), initial 217 States (of an automaton), sink 219 Stilwell, John 197 SUM 26 Sum of counting numbers 17 Sum of odd numbers 16 143—145 Sum of squares 124 144—146 Sum, closed 147 Tangent to a circle 66—67 Tennis 2—4 Ternary expansion 36 Tessellation 64—65 tetrahedron 195 Theory of special relativity 54 Thought experiment 117 topology 63 134 Torus 133—135
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