# 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