# catacaustic

Given a plane curve^{} $\gamma $, its *catacaustic ^{}* (Greek $\varkappa \alpha \tau \stackrel{\xb4}{\alpha}\varkappa \alpha \upsilon \sigma \tau \iota \varkappa \stackrel{\xb4}{o}\varsigma $ ‘burning along’) is the envelope

^{}of a family of rays reflected from $\gamma $ after having emanated from a point (which may be infinitely far, in which case the rays are initially parallel

^{}).

For example, the catacaustic of a logarithmic spiral^{} reflecting the rays emanating from the origin is a congruent spiral. The catacaustic of the exponential curve (http://planetmath.org/ExponentialFunction) $y={e}^{x}$ reflecting the vertical rays $x=t$ is the catenary^{} $y=\mathrm{cosh}(x+1)$.

Title | catacaustic |

Canonical name | Catacaustic |

Date of creation | 2013-03-22 18:52:56 |

Last modified on | 2013-03-22 18:52:56 |

Owner | pahio (2872) |

Last modified by | pahio (2872) |

Numerical id | 10 |

Author | pahio (2872) |

Entry type | Definition |

Classification | msc 53A04 |

Classification | msc 51N20 |

Classification | msc 26B05 |

Classification | msc 26A24 |

Synonym | caustic |

Related topic | HeronsPrinciple |

Related topic | ExampleOfFindingCatacaustic |