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catacaustic

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\begin{document}
Given a plane curve $\gamma$, its \emph{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 \PMlinkescapetext{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 \PMlinkname{exponential curve}{ExponentialFunction} \,$y = e^x$\, reflecting the vertical rays \,$x = t$\, is the catenary \,$y = \cosh(x\!+\!1)$.
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