# 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

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

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 |