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| Ïîèñê ïî óêàçàòåëÿì |
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| Polya G. — Mathematical Discovery: On Understanding, Learning and Teaching Problem Solving Combined Edition |
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| Ïðåäìåòíûé óêàçàòåëü |
'Blind Man's Rule', (Euler) 1 55
5-prism 2 151 154
A priori 1 119
abbreviations 1 xvii
Abel, Niels Henrik 1 188 2
Abracadabra 1 68—73
Abstraction 1 30 56
Adam, Charles 1 56
Aeppli, Alfred 1 xiii
Age of Reason (The) 2 60—61
Alexanderson, Gerald L. 1 vii xiii xvi
Algebra, for solving word problems 1 22 24
Alternating procedure 2 50—51
American Mathematical Monthly 2 112
Analogue, to Heron's theorem 1 45
Analogue, to Pythagoras' theorem 1 34 45
Analogy 1 13 2 52 86 124 149 H I II 27—28 see specialization
Analogy, binomial and polynomial coefficients 1 87—88
Analogy, of Heron's theorem 1 45
Analogy, of Pythagoras' theorem 1 34 45 H
Analogy, Pascal's and Leibnitz's triangles 1 88—90
Analogy, plane and solid geometry 1 12—13 50—51 83 2 108 H 235 I 45—47
Analysis 2 23 31 see
Angle, dihedral 1 12 2
Angle, trihedral 1 12
Anticipation 1 58—59
Aphorismen 2 99
Archimedes 1 38 44 57 98 2 163 H I 166—167
Area of triangle 1 34—35
Ariadne, The Thread of 1 148
Aristotle 2 71
Arithmetic mean 1 98
Ars Conjectandi 1 76
Ass of Buridan (The) 2 161—162
Auxiliary problem 1 18 2 96 H
Auxiliary problem, equivalent 2 37—39 H
Auxiliary problem, figures 1 14—15
Auxiliary problem, more, or less, ambitious 2 39—40 H
Auxiliary problem, remoter 2 41—42
Baron, Julius G. 2 202
Beckenbach, E.F. 2 175
Bernoulli, Jacob 1 76
Bernoulli, polynomials 1 62—68
Binomial coefficients 1 71—75
Binomial formula 1 63 65 67
Binomial theorem 1 75 91—93
Bolzano, Bernard 2 184 H
Borel, Emile 2 127
Boutroux, P. (and L.Brunschvicg) 1 67
Bradley 2 71
Bright idea 1 15 23 62 2 H
Brunschvicg, L. (and P.Boutroux) 1 67
Buridan 2 161
Butler, Samuel 2 60
Carbon atom (the) 2 188
Carroll, Lewis 1 41
Carry out your plan 2 7 31 H
Cartesian pattern 1 22—59
Cartesian pattern, classroom examples 1 29—32
Cartesian pattern, geometric examples 1 32—37
Cartesian pattern, wider scope 1 129—133
Case history 1 vi 9
Cavalieri 2 32 183
Ceteris paribus 2 93
Chains of equivalent problems 2 38—39
Checkmate in two moves 1 152
Choice between three plans 2 32
Circle, circumscribed 1 5
Circle, inscribed 1 5
Classroom examples of Cartesian pattern 1 29—32
Comparison of solutions to a word problem 1 25
Conclusion 1 121 2 H
Conclusion, how can you prove such a 2 26 34
Condition 1 4 119—120 129—133 2 78 H see data condition"
Condition, clauses 1 4 122
Condition, express by equations see "Pattern Cartesian"
Condition, keep only a part 1 4 17 33 147 2 H
Condition, major clause 1 140
Condition, redundant 1 42—44 I 200—202
Condition, split the condition 1 5 6 19 27 129—133 150
Condition, sufficient, or insufficient, to determine the unknown 1 18 41—42 54 55 57—58 H I
Condition, the clause to begin with 1 138—142 148—149 151—153
Condition, using the whole see "Did you use all of the data?"
Conjecture see "Guess"
Consistence, Independence and 1 57—58
Constructions, geometric 1 20
Constructions, ruler and compass 1 3 20 32
Contained in, sets 1 20
Continuous transition 1 10 37 2
Could you solve part of the problem? 1 40 45
Counterexample 2 49—51 H
Courant, Richard 1 20 32
Critique of Pure Reason 1 99
Crossword puzzle 1 32—33 131 138—139 2
cube 2 151 154
Cuboctahedron 2 205
Curvilinear quadrilateral 1 44
Dante 2 54 I
DATA 1 3 119—120 127—128 2 H see data condition"
Data, derive something useful from 1 7 2 H
Data, to determine this kind of unknown 2 85—86
Data, variation of 1 10 31 101 H
de Montaigne, Michel 2 102
Decimals, periodic 2 164—165
Decisions 2 65—66
Definition 2 81 83 H
Denk, Franz 2 138 207
Descartes, on polyhedra 2 154 I
Descartes, Rene 1 1 22 23 27—28 55—59 61 115 129 2 12 36 77 78 126—127 149—158 184 H II 142
Descartes, Rules for the Direction of the Mind 1 22 26—28 55—56 58—59 2
Descriptive geometry 2 12
Deus ex machina 1 64 2 II
Diagram 2 68—71
Did you use all the data (the whole condition, the whole hypothesis)? 1 17 102 2 H 152 II 162—163
Difference equations, homogeneous 1 108
Differential equations 1 96
Differential equations, homogeneous linear 1 108
Dihedral angle 1 12 2
Diophantine problem 1 55
Diophantus 2 187
Discipline of the mind 2 12 77—88
Discovery, Story of a Little 1 60—62
Do not commit yourself 2 34
Do you know a related problem? 2 80 H
dodecahedron 2 153—154
Dodecahedron, rhombic 2 205
Dodgson, Charles 1 41
Dudeney, H.E. 1 207
Duncan, Isadora 2 134
Duncker, Karl 2 65 67 72 H
Economy 2 91—92 96
Egyptian Problem, An 1 48
Einstein 2 102
Elwes, R.H.H. 2 134
Empty set 1 20
Equal sets 1 20
Equations, as many as unknowns 1 54
Equations, differential 1 96
Equations, fewer than unknowns 1 55
Equations, homogeneous linear difference 1 108
Equations, homogeneous linear differential 1 108
Equations, incompatible 1 58
Equations, inconsistent system of 1 58
Equations, more than unknowns 1 54
Equations, n in n unknowns 1 142—145
Equations, self-contradictory system of 1 58
Equations, setting up 1 26
Equations, system of 1 28 2
Equations, system of four 1 129—130
Equivalent problems 1 125 2
| Euclid 1 3 43 104 118 122 127 2 36 85—86 152 184 I
Euclidean constructions 1 3 20 32
Euler, 'Blind Man's Rule' 1 55
Euler, Leonhard (1707—1783) 1 46—48 55 72 2 I 9 18—22 30—34 90—102 106—107 121 II 95—96
Euler, line 2 48
Euler, on polyhedra 2 149—158 176 I 52—58
Example, from a puzzle 1 39—40
Example, from physics 1 37—39
Example, pattern 1 4—6
Example, puzzling (cartesian) 1 41—44
Expanding pattern 1 40
Exploring the neighborhood 2 194
Extrapolation 1 100
Extreme case 1 10
Fact and conjecture 2 168
Fejes-Toth, L. 2 164
Fibonacci, (Leonardo of Pisa) 1 49
Fibonacci, numbers 1 109 2
Fibonacci, numbers (Binet formulas for) 1 196—197
flexibility 2 35 II
Folding, cardboard 1 12—13
France, Anatole 2 142
Frustum (of a right pyramid) 2 2—10
Function 1 99—100
Galileo 1 109 2 I 194—196
Galois, Evariste 2 88
Gauss, Carl Friedrich 1 60—62 2 I
Generalization 1 25 48 53 62 64 77 81 83 88 92 111 112 175 2 152 H I 22—23 II
Generalization and specialization 2 51—52
Generalization, general formulation advantageous 1 69
Generalization, letters for numbers 1 25 44 162 H
Generalization, observe and generalize 1 76 84 2 152 H I
Generalization, specialization, and analogy 2 53 80 124 I
Genetic principle 2 132—133
Genius, the expert, and the beginner 2 97
Geometric constructions 1 3—4 20
Geometric mean 1 98
Geometry, descriptive 1 12
Geometry, plane 1 48
Geometry, solid 1 34 50—51 2
Gestalt 2 68
Given 1 3
Go back to definitions 2 194
Goldbach, Christian 1 121 I
Gothic tracery 1 17 32—33 44
Graphic time table 1 52—54
Guess 1 34 46 79 95 2 105 124 143—168 I II
Guess, examine your guess 2 156—157 168 H see "Induction"
Hadamard, Jacques 1 113 2 184 H 199
Haeckel, Ernest 2 133
Harmonic mean 1 98
Harmonic triangle 1 88—89
Hartkopf, Werner 1 ix 2 184
Have you seen it before? 1 147
Heath, T.L. 1 98
Hermite, Charles 2 143
Heron's (also Hero's) theorem 1 34—35 2 158 see
Heron's (also Hero's) theorem, analogue to 1 45
Heuristic 2 10
Heuristic, rat's maze 2 74
Hilbert, David 2 127
Hilgard, E.R. 2 100
Hilton, Peter 1 vii xvi 2
Hobbes, Thomas 2 22
Homothetic figures 1 9
How can you get THIS kind of thing (unknown, conclusion)? 1 34 36 110 2 6 29—30 79 86 see or kind "Theorem or
Hypothesis 1 121
Hypothesis and conclusion 1 121 125 127 2 78 94 H
Hypothesis to derive this conclusion 2 85—86
icosahedron 2 153—154
If you cannot solve the proposed problem 1 10 69 24 H
Incompatible equations 1 58
Inconsistent system of equations 1 58
Independence and consistence 1 57—58
Indeterminate problem 1 99—101
Indeterminate system of equations 1 58
Induction 1 91—92 183 2 H I I II see observe
Induction, fundamental inductive pattern (heuristic syllogism) H 186—190 II
Induction, mathematical 1 73—75
Induction, observe and explain regularities 1 94 189 190 2 181 H I
Induction, verification (in particular cases, of consequences) 1 92 2 153 154 H
Inequality 1 51
Inside help, outside help 2 135—137 H
Interpolation 1 99—101
Interpretation 1 30 44
Interpretation, mechanical 1 146—148
Interpretation, optical 1 142—146
Interpretation, reinterpretation 1 149—155
Intersection, of sets 1 21
Inversion of a power series 1 95
Is there a solution? 2 79 H see sufficient or to
Isolation and combination 2 68—69
Isoperimetric problem 2 144—145
James, William 1 117 2 H
Kant, Immanuel 2 99 103
Keep part of the condition 1 33
Kepler, Johannes 2 123 181 I 196—198
Key facts 2 81 85
Key figure 1 167
Keynes, J.M. 2 161
Klein, Felix 2 126
Kohler, Wolfgang 2 36 H
Krauss, F. 2 184 H
Lagrange, interpolation formula 1 101—104
Lagrange, Joseph 1 104 195
Lakatos, Imre 2 51 127 184
Language, algebraic (mathematical) 1 24 2 124 H
Language, algebraic (mathematical), of geometric figures 2 85 124—125
Lattice point 1 202
leap years 2 194
Learning, Three principles of 2 102—104
Leibnitz's Harmonic Triangle 1 88—89
Leonardo of Pisa (Fibonacci) 1 49
Lichtenberg, Georg 2 61 99 103
Lighthouses, Three 1 16—17
Lindemann, Ferdinand 1 126
linear combination 1 106—107
Listening posts, three 1 19
Loci, patterns of 1 3—21
Loci, two for a function 1 140—142
Locus 1 4 5 133
Loewner, Charles 1 xv 2
Logothetti, Dave 1 xvi
Look at the unknown 2 87 H see or kind
Mach, Ernst 2 184 H I
Magic square 1 149
Maps 2 129—132
Mariotte 2 62
Mathematical induction 1 73—75 82 H I
Mathematische Schriften 2 99
Maxwell, James Clerk 2 133
Mean, arithmetic I 98
Mean, geometric 1 98
Mean, harmonic 1 98
Medians of a triangle 1 11
Meiklejohn, J.M.D. 2 99
Mental inertia I 63
metaphors 2 1—2
method see also "Pattern" "Result
Method of successive approximations 1 26
Method of undetermined coefficients 1 93—94
Mice and men 2 75—76
Mobilization and organization 1 57 2 66—67 73 H
Mobilization and organization, diagram (How we think) 2 69
Modus operandi 1 122
Monroe, Marilyn 2 134
Morphological structure 2 155
Mozart, Wolfgang 2 102
Multiplicity of approaches 1 75 83 109
n-double-pyramid 2 153—154
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