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| Polya G. — Mathematical Discovery: On Understanding, Learning and Teaching Problem Solving Combined Edition |
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| Ïðåäìåòíûé óêàçàòåëü |
n-prism 2 153—154
n-pyramid 2 153—154
Napoleon's problem 2 26—28
Newman, J.R. 1 48 91
Newton, Sir Isaac (1643—1727) 1 46—49 53 54 91—92 188 2 89 181 I 87
Nicolet, J.L. 2 203
Niven, Ivan 2 181
No solution 1 18
Notation, triangle 1 16
Number, pyramidal 1 85
Number, square 1 85
Number, triangular 1 84—85
Numbers, Fibonacci 1 109
Numbers, trapezoidal 2 166—167
Numbers, triangular 2 166
octahedron 2 151 154
Octahedron, volume of 1 51
One more high school research project 2 195
Ontogeny 2 132—133
Out of the blue 1 64 H II
Paine, Thomas 2 60—61
Paper cutting 1 45
Pappus 1 9 2 31 184 207 H
Paradigmatic teaching 2 123
Part suggests the whole 2 71—72 149
Pascal, Blaise 1 67 70—75 84—89 176
Pattern, Cartesian 1 22—23 26—29 129—133 H
Pattern, of auxiliary figures 1 14—15 H
Pattern, of mathematical induction 1 73—75 82 H I
Pattern, of recursion 1 66—68 142—146
Pattern, of similar figures 1 9—10 15 H
Pattern, of superposition 1 105—106 113
Pattern, of three loci 1 19
Pattern, of two loci 1 4—5 6 15 19 133—138
Pattern, of undetermined coefficients 1 93—97
Pattern, of working backward 2 13—14 16 22—24 29—31 44 H 225—232
Pattern, of working forward 2 8 17—18 29—31
Pedersen, Jean 1 vii xvi
Periodic decimals 2 164—165
Persistence 2 92 96
Photometer 2 188
Phylogeny 2 132—133
Physics, an example from 1 37—39
Plane geometry 1 48
Plans and programs 2 10 22—35
Plausible reasoning 2 157
Plums and plans (Of) 2 97
Polyhedra 2 149—160
Polyhedron, flattened 2 155
Polyhedron, n faces 1 83
Polyhedron, six faces 1 83
Power series 1 90—91
Power series, inversion of 1 95
Prevision 2 64—65 69
Principle of Nonsufficient Reason 2 160—163 I
Principle, genetic 2 132—133
Prismoidal formula 1 110—113
Problem 1 117—118
Problem(s), auxiliary 2 11 36
Problem(s), chess 1 152
Problem(s), classification of 1 118—119
Problem(s), Diophantine 1 55
Problem(s), nonmathematical 1 151—152
Problem(s), rate 1 29—32
Problem(s), translator's 1 152
Problem, equivalent 1 4 125 2 H
Problem, formulation 1 99—101 2 108
Problem, indeterminate 1 99—101
Problem, principal parts 1 120 121 2 H
Problem, related 1 4 80 H
Problem, related and simpler 1 69
Problem, related and solved before 1 110 2 H
Problem, solve part of the proposed 1 6 7 8 11 40 45 H
Problem, strip it 1 56—57
Problem, take the problem as almost solved I 127
Problem, take the problem as solved 1 6—9 11 15 27 45 164 H 146—147
Problem, to find 1 119—120 132 H
Problem, to prove 1 119 120—121 H
Problem, with the same, or a similar, kind of unknown 2 44—45 82 85 86 95 H
Proclus 2 36
Productive thinking, creative thinking 2 87—88 97
PROGRAM 2 25 28
Progressive planning, see Pattern or working forward Proximity 2 63 II
Puzzles 1 39—40 45—46 137—140 143—144 149 H
Puzzles, crossword 1 131—132 137—139 147—148 2 61 172 H
Pyramid, volume of 1 106 2 39
Pyramidal number 1 85
Pythagoras' theorem see also "Analogy"
Pythagoras' theorem, analogue in solid geometry 1 34—37
Pythagoras' theorem, another analogue to 1 45
Quadrilateral, curvilinear 1 44
Rate problems, classroom examples 1 29—32
Rationality 2 90—91 96
Rationals and irrationals 2 125—126
Recognizing and remembering 2 67
Recursion formula 1 66—68 73 88 109 142—145 191 I 102 104
Reduce the problem 1 5
Reduction 1 5 6
Reduction, ad absurdum H 162—171
Reduction, bilateral 2 37—38 H
Reduction, convertible see "Bilateral"
Reduction, equivalent see "Bilateral"
Reduction, unilateral 2 39—40 H
redundant data 1 44
Region of search 2 65
Regressive planning 2 23 see
Regula Caeci 1 55
Related figure 1 15
Related problem 1 10 110
Relevancy 2 63
Relevant knowledge 1 29 38 57 159 2 193 H 159
Respice finem 2 43—46
Restate the problem 2 15—17 84 H 88
Result or method 1 81 98 107 192 H
Retrospective discussion 2 106 H
Rhombic dodecahedron 2 205
Robbins, Herbert 1 20 32
Rule, Blind Man's (Euler) 1 55
Rule, Descartes' 1 55—57
Rule, Simpson's 1 112
Rules 2 89—90 97
Rules for 'The Direction of the Mind' 1 22 2126
Rules of discovery 2 89—98 H
Rules of plausible reasoning II 109—111
Rules of preference 2 93
Rules of teaching 2 104—106 H
Rules, Zermelo's 2 141—142
Salvaging 2 188
Schlegel diagram (flattened polyhedron) 2 155
| Schur, Issai 2 143
Scientific method, guess and test 2 156
Self-contradictory, system of equations 1 58
Sequence and consequence 1 126
Sequence, well-ordered 1 67
Series, power 1 90—91
Sets 1 20—21
Setting up equations see "Pattern Cartesian"
Shaw, Bernard 2 134
Signum x 1 124—125
Similarly located (homothetic) 1 9
Simpson's rule 1 112
Socratic (method, dialogue) 2 103 104 107
Solid geometry 1 34 50—51 2
Solution 1 120 126—127 H see
Solution, looking back at the solution 1 18 H
Specialization 2 51 124 H I
Specialization, concrete interpretation H 197
Specialization, extreme special case H 192—196 I
Specialization, leading particular case 1 106 113 I
Specialization, leading particular case, next particular case 1 63
Specialization, leading particular case, particular case equivalent to general case 1 79 I
Specialization, leading particular case, representative special case 1 78 178 I
Specialization, leading particular case, special situation 1 102 104 see specialization and
Sphere, circumscribed about tetrahedron 1 19
Spherical triangles 1 12
Spherometer 1 51—52
Spinoza, Baruch 2 134
Square number 1 85
Squaring the circle 1 126
St. Augustine 2 97
Steiner, Jacob 2 175
Stepping stone 1 8—9 11 14 15 H
Strict reasoning 2 126—129 H
Style of work 2 97—98
subproblem see "Auxiliary problem"
Subset 1 20
Successive approximations 1 26
Sufficient condition 1 59 41—42
Sum of consecutive odd positive integers 2 167
Sum of first n integers 1 60—62
Sum of first n odd numbers 1 81
Sum of first n squares 1 62—64
Sum of like powers of the first n integers 1 64—68
Superposition 1 8 106—107 99—113
Supplementing and regrouping 2 67—69
Sussanan, Irving 2 209
Symmetry 1 153 159 207 208 2 160—163 H I 187—188
Synthesis 2 23 see
System of equations 1 28 2
Szegoe, Gabor 2 135 184 207
Take the problem as solved (wishful thinking) 1 6—9 11 27 45
Tangents to circles 1 10
Tannery, Paul (and Charles Adam) 1 56
Teaching is an art 2 101—102
Teaching is not a science 2 99—100
Teaching, the aim of 2 100—101
Teaching, three principles of 2 104
Teaching, what should we teach? 2 132
Ten Commandments for Teachers 2 116—120
Term paper 2 140—141
Test your conjecture see "Guess examine"
tetrahedron 1 34 111—112 2 154
Tetrahedron, circumscribe a sphere about 1 19
Tetrahedron, volume of 1 51 106 109—110
Theorem (proposition) 1 121
Theorem (proposition), prove, or disprove 1 120—121 2 H
Theorem (proposition), stronger (possible ground) 2 47 II
Theorem (proposition), weaker (consequence) 2 47—48 II 18—19
Theorem (proposition), with the same, or a similar, conclusion 2 45 82 85 86 95 H
Theories of Learning 2 100
Three lighthouses 1 16—17
Three listening posts 1 19
Timetable, graphic 1 52—54
Tower (polyhedron) 2 151 154
Traite du triangle arithmetique 1 71
Transition, continuous 1 37
Translator's problem 1 152
Trapezoidal numbers 2 166—167
Trial and error 1 26
Triangle, area of 1 34—35
Triangle, Leibnitz's harmonic 1 88—89
Triangle, medians of 1 11
Triangle, notation for 1 16
Triangle, Pascal's 1 70—75
Triangular number 1 84—85 2
Trihedral angle 1 12
Trinomial coefficients 1 87—88
Understand the problem 1 27
Undetermined coefficients, method of 1 93—94
Unilateral reduction 2 39—42
Union, of sets 1 21
Unique solution 1 58—59
Universal method 1 22
UNKNOWN 1 3 119 2 H
Unknown, auxiliary 1 31 2 H
Unknown, data, condition 1 5 8 10 11 27 119—120 125 2 94 H 214
Unknown, how to find this kind of unknown 1 34 36 110 2 6 29—30 79 86 H
Unknown, multicomponent 1 122
Unknown, multipartite 1 122
Unknown, operational 1 126
van Beethoven, Ludwig 2 102
Van der Waerden, B.L. 2 187
Variation of the data 1 10 31 101
Vector-space 1 107
Volume of a 'hoof' 2 32
Volume of frustum of right pyramid 2 2—10
Volume of octahedron 1 51
Volume of prismoid 1 110—113
Volume of pyramid 1 106 2 39—40
Volume of tetrahedron 1 51 106 109—110
von Leibnitz, Gottfried 1 46 83 88 89 91 111 125—126 129 148 2 50 62—63 99 168 184 H I
Wagenschein, Martin 2 123 186
Wallis, John 1 91
Well-ordered sequence 1 67
Wertheimer, Max 2 100
Weyl, Hermann 2 128
What are such things (data hypothesis) good for? 2 30 79—80 H see derive
What do you want? 2 3 44 78 H see "Look "Unknown Data condition" "Conclusion" "Hypothesis
What have you? 2 3 78 H
What is Mathematics? 1 20 32 see "Unknown data condition" "Hypothesis" "Hypothesis
Wise man begins in the end 2 31
Wishful thinking 1 6—8
Wittenberg, A.I. 2 123 133 209
Working backward, from the unknown to the data see "Pattern of working backward"
Working forward, from the data to the unknown see "Pattern of working forward"
Working from inside, from outside 2 73 81
Working of the mind 2 11 62—76
Zermelo's rules 2 141—142
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