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. This construction of the witch is a reflection of the
one mentioned in the biography across the line y = x.
Famous Curves from the MacTutor History of Mathematics web
of Agnesi by Eric W. Weisstein.
The Witch of Agnesi by Daphne Golden and Melissa Hanzsek-Brill,
from a Department of Mathematics Education class at the
University of Georgia.