Definition:Witch of Agnesi
Let $OA$ be extended to cut the tangent to the circle through $M$ at $N$.
Various properties of the Witch of Agnesi are as follows.
- It is defined for all $x$.
- $0 < y \le 2 a$.
- $y$ reaches its maximum at $x = 0$.
- The curvature $K$ of the curve is such that $0 \le K \le \dfrac 1 a$, and it achieves that maximum at $x = 0$.
Also known as
The Witch of Agnesi is also known as the versiera.
- Results about Witch of Agnesi can be found here.
Source of Name
This entry was named for Maria Gaëtana Agnesi.
It had previously been written about by others, for example Pierre de Fermat.
The word witch appears to be a mistranslation from the Italian vertere (to turn: the term comes from the rope used to turn a sail) as avversiera which means witch or she-devil (from the same root as the word adversary, an archaic soubriquet for Satan).
It has been suggested that the initial misnaming may have been mischievous.
When referred to in other languages, the term witch is not seen, and the less colorful term curve of Agnesi is usually used instead.
Note the name Agnesi is Italian: its pronunciation is something like an-ye-zi, and never in the apparently obvious way ag-nee-zee.