A Trio of Parabola Constructions

In my prior blog posts, I’ve presented methods for constructing ellipses  using Web Sketchpad and paper folding. The other conic sections are feeling a bit left out, so let’s explore some techniques for constructing parabolas.

All three Web Sketchpad models below (and here) are based on the distance definition of a parabola: The set of points equidistant from a fixed point (the focus) and a fixed line (the directrix).

Experiment with the interactive models and think about why they  generate parabolas. The rhombus construction is based on an illustration found in the 17th-century Dutch mathematician Frans van Schooten’s manuscript, Sive de Organica Conicarum Sectionum in Plano Descriptione, Tractatus (A Treatise on Devices for Drawing Conic Sections). Van Schooten’s beautiful picture is below.

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