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# 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 fixed 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 $y=e^{x}$ reflecting the vertical rays $x=t$ is the catenary $y=\cosh(x\!+\!1)$.

Related:

HeronsPrinciple, ExampleOfFindingCatacaustic

Synonym:

caustic

Type of Math Object:

Definition

Major Section:

Reference

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## Mathematics Subject Classification

53A04*no label found*51N20

*no label found*26B05

*no label found*26A24

*no label found*

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