The catacaustic of one arch of a cycloid
given parametrically as

is a complicated expression for an arbitrary radiant point. For the case of the radiant point at
,
however, the catacaustic becomes

which is, rather amazingly, precisely two arches cycloid
with identical beginning and endpoints and twice the period.

## See also

Catacaustic,

Cycloid
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## Cite this as:

Weisstein, Eric W. "Cycloid Catacaustic."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/CycloidCatacaustic.html

## Subject classifications