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