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Van Schooten's rhombus linkage for parabolas

Move point G to trace the parabola.

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Frans Van Schooten published Exercitationum Mathematicorum in 1657; it was a textbook explaining the material in Rene Descartes's Geometry in an understandable way.
This applet shows Van Schooten's illustration of a machine for drawing parabolas. Physically, the rhombus is necessary; mathematically, all that is needed is the perpendicular bisector of segment BG, or, equivalently, a (variable) isosceles triangle with base BG. The rhombus ensures that points F and H lie on the perpendicular bisector of BG.

Note how accurate Van Schooten's drawing is. Physically, the rhombus could not close completely because of the connectors at B and G. This doesn't happen within the rectangle of the picture. Zoom out, and you can drag G so that the rhombus disappears.

Susan Addington, Created with GeoGebra


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Last updated January 16, 2010

Copyright 2009 David Dennis and Susan Addington. All rights reserved.