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

$$y=\frac{8c}{4c^2+x^2}$$

in the Cartesian plane. If we set $c=\frac{1}{2}$, the equation simplifies to $y=\frac{1}{1+x^2}$. 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