Given a plane curveMathworldPlanetmath γ, its catacausticMathworldPlanetmath (Greek ϰατα´ϰαυστιϰo´ς ‘burning along’) is the envelopeMathworldPlanetmath of a family of rays reflected from γ after having emanated from a point (which may be infinitely far, in which case the rays are initially parallelMathworldPlanetmathPlanetmath).

For example, the catacaustic of a logarithmic spiralMathworldPlanetmath reflecting the rays emanating from the origin is a congruent spiral.  The catacaustic of the exponential curve (  y=ex  reflecting the vertical rays  x=t  is the catenaryMathworldPlanetmathy=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