We use MathJax

## Witch of Agnesi

In the graph above, a green circle of radius $a$ is centered
at $(0,a)$, and a green horizontal line is $2a$ units above
the $x$-axis, tangent to the circle. The red line drawn through the origin will
intersect both the circle (at a point other than the origin) and the
horizontal line. Using the $x$-coordinate from the intersection with
the horizontal line, and the $y$-coordinate from the intersection
with the circle, the blue curve given by the equation
$x^2y=4a^2(2a-y)$ is generated.

Maria Gaetana Agnesi (1718-1799) of Milan received her early
education
through tutors provided by her father, and later through self-study and
personal
contacts. Drawn toward mathematics, she compiled much of the
mathematics
then known in her most important work, *Instituzioni Analitiche*,
in
1748. Her achievement brought her an appointment to the
University of
Bologna, although she never filled the position. Included in her
work was a discussion of a curve called *la versiera*, or twisted
curve,
earlier studied by Pierre de Fermat (1601-1665) and by Guido Grandi
(1671-1742). Agnesi's work was eventually translated into
English, and at
that time the term *la versiera* was corrupted into *l'aversiera*,
or
witch.
So the English translator referred to the curve as the
Witch of Agnesi.