How to Solve it: A New Aspect of Mathematical Method |
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Page 17
A New Aspect of Mathematical Method George Pólya. parallelepiped becomes a parallelogram . If you put co in your formula , do you obtain the correct formula for the diagonal of the rectangular parallelogram ? " " If the height c ...
A New Aspect of Mathematical Method George Pólya. parallelepiped becomes a parallelogram . If you put co in your formula , do you obtain the correct formula for the diagonal of the rectangular parallelogram ? " " If the height c ...
Page 20
... Parallelogram . " The students , even if they are very slow and indiffer- ent , and were not able to guess anything before , are obliged finally to contribute at least a minute part of the idea . Besides , if the students are so slow ...
... Parallelogram . " The students , even if they are very slow and indiffer- ent , and were not able to guess anything before , are obliged finally to contribute at least a minute part of the idea . Besides , if the students are so slow ...
Page 37
... parallelogram is analogous to a rec- tangular parallelepiped . In fact , the relations between the sides of the parallelogram are similar to those be- tween the faces of the parallelepiped : Each side of the parallelogram is parallel to ...
... parallelogram is analogous to a rec- tangular parallelepiped . In fact , the relations between the sides of the parallelogram are similar to those be- tween the faces of the parallelepiped : Each side of the parallelogram is parallel to ...
Contents
IN THE CLASSROOM | 1 |
Understanding the problem | 7 |
Example | 13 |
Copyright | |
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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