Folded Paper, Dynamic Geometry, and Proof: A Three-Tier Approach to the Conics (original) (raw)

Abstract

Some of the most lasting impressions that we retain from the study of circles come from our informal exposure to them in daily life. It may have been years since we learned, and perhaps forgot, the equation x2 + y2 = r2, but we can still summon our hands-on experiences to remember the essential features of a circle. The notion of a circle's having a center that is equidistant from all its points gets reinforced whenever we use a compass or twirl a rope or cord with our fingers. The symmetry of a circle becomes apparent each time we turn a knob or struggle to loosen a lid on a jar.

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