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. You’ll find many more of van Schooten’s constructions in my book Exploring Conic Sections with The Geometer’s Sketchpad.

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