This is a prototype of JavaSketchpad, a World-Wide-Web component of The Geometer's Sketchpad. Copyright ©1990-1997 by Key Curriculum Press, Inc. All rights reserved. Portions of this work are being funded by the National Science Foundation (awards DMI 9561674 & 9623018 ).
Credits. This page, and the Geometer's Sketchpad document on which it is based, is from the WWW project A Visual Dictionary of Special Plane Curves, Copyright 1995, 1996 by Xah Lee (email@example.com). It can be freely distributed provided this information is intact.
The Witch of Agnesi is defined as the curve traced by X as Drag Me moves around the circle. You can drag Drag Me with the mouse, or click Animate to move it around the circle. Click Show Trace to begin tracing point X as it moves; click Hide Trace to stop. You can also drag any other red point, or while the sketch is animating, press '>' or '<' keys to speed up and slow down the animation. Click the red X in the lower-right corner to clear any visible traces.
Step by step description
(a is the scaling factor. Geometrically, it's the radius of the circle on which the Witch is constructed.)
Studied by Maria Gaetana Agnesi (1718-1799) in 1748. Also studied by Fermat (1666), and Guido Grandi (1703). The name of this curve has a colorful history. "Versaria" is the name given by Grandi, meaning "turning in every direction". In the course of time the word versaria took on another meaning. The Latin words adversaria, and by aphaeresis, versaria, signify a female that is contrary to God. Thus gradually the curve versaria came to be known in English as "the witch."
Return to the JavaSketchpad Gallery.