curve of Agnesi

Given a real constant c, the curve of Agnesi (often called witch of Agnesi in English) is the result of plotting the equation


in the Cartesian plane. If we set c=12, the equation simplifies to y=11+x2. Another way of drawing the curve employs a circle of radius c.

In the following diagram, the associated circle is shown in light gray.

(This diagram was made with Grapher 1.1 for Mac OS X).

This curve was first studied by Pierre de Fermat, but Maria Gaetana Agnesi later studied it in greater detail and mentioned it in her book Instituzioni Analitiche.

Title curve of Agnesi
Canonical name CurveOfAgnesi
Date of creation 2013-03-22 16:40:56
Last modified on 2013-03-22 16:40:56
Owner CompositeFan (12809)
Last modified by CompositeFan (12809)
Numerical id 5
Author CompositeFan (12809)
Entry type Definition
Classification msc 51N20
Synonym Agnesi’s curve
Synonym witch of Agnesi
Synonym Agnesi’s witch
Synonym averisera
Synonym avversiera
Synonym cubique d’Agnesi
Synonym agnésienne
Synonym agnesienne
Related topic AsymptoteOfLamesCubic