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IN THE CLASSROOM
Understanding the problem
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altitude 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 isosceles know a related knowledge length letters look MATHEMATICAL INDUCTION mathematical problems means median planes method numbers object obtain octahedron original problem pappus parabola parallel 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 satisfy Separate the various side signs solid geometry solution sort sphere square step straight line student syllogism teacher tetrahedron theorem tion try to think vertex vertices wish word