How to Solve it: A New Aspect of Mathematical Method |
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Page 42
... method of the simpler analogous problem whose solution we imi- tated point by point . Under 6 , we used the result of the simpler analogous problem , and we did not care how this result had been obtained . Sometimes , we may be able to ...
... method of the simpler analogous problem whose solution we imi- tated point by point . Under 6 , we used the result of the simpler analogous problem , and we did not care how this result had been obtained . Sometimes , we may be able to ...
Page 225
... method of analy- sis , or method of " working backwards . " This method , by the way , is discussed also elsewhere in the present book , under the name of PAPPUS to whom we owe an Working Backwards 225 Working backwards.
... method of analy- sis , or method of " working backwards . " This method , by the way , is discussed also elsewhere in the present book , under the name of PAPPUS to whom we owe an Working Backwards 225 Working backwards.
Page 230
... method of analysis . The tradition may not be quite reliable but , at any rate , if the method was not invented by Plato , some Greek scholar found it necessary to attribute its invention to a philosophical genius . There is certainly ...
... method of analysis . The tradition may not be quite reliable but , at any rate , if the method was not invented by Plato , some Greek scholar found it necessary to attribute its invention to a philosophical genius . There is certainly ...
Contents
IN THE CLASSROOM | 1 |
Understanding the problem | 7 |
Example | 13 |
Copyright | |
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Common terms and phrases
altitude analogous problem analogy angle Archimedes argument auxiliary element auxiliary problem base center of gravity conclusion condition connection consider construction definition derive desirable discuss Draw a figure edge equation essential Euclid's Elements examine example express fact foregoing formerly solved problem formula frustum given guess heuristic reasoning hypothesis important indirect proof induction introduce invention know a related knowledge length look MATHEMATICAL INDUCTION mathematical problems means median planes method numbers object obtain octahedron original problem Pappus parabola parallelepiped parallelogram perimeter plane geometry plausible possible present prime prob problem to find problem to prove procedure progress proposed problem questions and suggestions reductio ad absurdum related problem restate result right triangle satisfied Separate the various side signs simpler analogous solid geometry solution sort sphere square step straight line student syllogism teacher tetrahedron theorem tion try to think vertex vertices wish word