The catacaustic of the natural logarithm 
specified parametrically as
 |  |  |
(1)
|
 |  |  |
(2)
|
is a complicated expression for an arbitrary radiant point.
However, for a point 
, the catacaustic
becomes
 |  |  |
(3)
|
 |  |  |
(4)
|
Making the substitution 
then gives the equivalent parametrization
 |  |  |
(5)
|
 |  |  |
(6)
|
which is the equation of a catenary.
