How to Solve it: A New Aspect of Mathematical Method |
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Page 48
... perimeter of the triangle . P FIG . 9 h p FIG . 10 A h We introduce suitable notation . Let a denote the given angle , h the given altitude drawn from the vertex A of α and p the given perimeter . We draw a figure in which we easily ...
... perimeter of the triangle . P FIG . 9 h p FIG . 10 A h We introduce suitable notation . Let a denote the given angle , h the given altitude drawn from the vertex A of α and p the given perimeter . We draw a figure in which we easily ...
Page 100
... perimeter , find the one that has the greatest area . What is the unknown ? A quadrilateral . What are the data ? The perimeter of the quadrilateral is given . What is the condition ? The required quadrilateral should have a greater ...
... perimeter , find the one that has the greatest area . What is the unknown ? A quadrilateral . What are the data ? The perimeter of the quadrilateral is given . What is the condition ? The required quadrilateral should have a greater ...
Page 101
... perimeter the square has the greatest area . " If we decide ourselves to examine this statement , the situation changes . Originally , we had a " problem to find . " After having formulated our guess , we have a " problem to prove ...
... perimeter the square has the greatest area . " If we decide ourselves to examine this statement , the situation changes . Originally , we had a " problem to find . " After having formulated our guess , we have a " problem to prove ...
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