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# 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.

Related:

AsymptoteOfLamesCubic

Synonym:

Agnesi's curve, witch of Agnesi, Agnesi's witch, averisera, avversiera, cubique d'Agnesi, agn\'esienne, agnesienne

Type of Math Object:

Definition

Major Section:

Reference

Groups audience:

## Mathematics Subject Classification

51N20*no label found*

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## Info

## Versions

(v5) by CompositeFan 2013-03-22

## Comments

## Diagram

I was going to tell you to avail yourself of the sandbox to make a diagram for this entry, but I see you've already done so, so that's good.