The catacaustic of the natural logarithm
specified parametrically as

is a complicated expression for an arbitrary radiant
point.

However, for a point , the catacaustic
becomes

Making the substitution then gives the equivalent parametrization

which is the equation of a catenary.

## See also

Catacaustic,

Catenary,

Natural Logarithm
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## References

Lawrence, J. D. *A Catalog of Special Plane Curves.* New York: Dover, p. 207, 1972.## Referenced
on Wolfram|Alpha

Natural Logarithm Catacaustic
## Cite this as:

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

## Subject classifications