Published by Maria Gaëtana Agnesi (1718-1799) in her best-known work Instituzioni analitiche ad uso della gioventù italiana (translated: Analytical Institutions for the Use of Italian Youth, 1748) the Witch of Agnesi is a versed sine curve. (A versed sine, or versine curve, is an outdated expression for 1 - cos x, which was commonly used to describe curves in early mathematics.) It is alternatively known as Cubique d'Agnesi (Agnesi's cubic), Agnésienne, or the Agnesi curve, and was studied by both Pierre de Fermat and Guido Grandi as early as 1703. Termed "versiera" by Agnesi, the name of the curve was mistranslated "wife of the devil" or "witch" and hence the name "Witch of Agnesi" stuck. The curve is often most described algebraically, parametrically, or geometrically.

To construct the Witch of Agnesi geometrically, first draw a circle of diameter d centered at (0,d...