Agnes Scott College

The Witch of Agnesi

The bell-shaped witch of Maria Agnesi can be constructed in the following way. Start with a circle of diameter a, centered at the point (0,a/2) on the y-axis. Choose a point A on the line y = a and connect it to the origin with a line segment. Call the point where the segment crosses the circle B. Let P be the point where the vertical line through A crosses the horizontal line through B. The witch is the curve traced by P as A moves along the line y = a. In the GeoGebra app below, you can click on the point A with your mouse and move it along the line y = a. This construction of the witch is a reflection of the one mentioned in the biography across the line y = x.

Web Resources

  1. Famous Curves from the MacTutor History of Mathematics Archive
  2. Witch of Agnesi by Eric W. Weisstein.
  3. The Witch of Agnesi by Daphne Golden and Melissa Hanzsek-Brill, from a Department of Mathematics Education class at the University of Georgia.

Return to biography of Maria Agnesi.