# catacaustic

Given a plane curve $\gamma$, its catacaustic (Greek $\varkappa\alpha\tau\acute{\alpha}\,\varkappa\alpha\upsilon\sigma\tau\iota% \varkappa\acute{o}\varsigma$ ‘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$y=\cosh(x\!+\!1)$.

 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