Abstract

One sign of a good problem is that it offers multiple revelations during its investigation. Another is that it can be approached mathematically in more than one way. Three related problems that meet both those criteria involve paper folding and conic sections. Each problem can be demonstrated easily with a sheet of wax paper or emulated by a geometry drawing program like The Geometer's Sketchpad, yet each contains interesting mathematics whose properties are established in nontrivial ways.

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