Given a plane curve
, its catacaustic (Greek
`burning along') is the envelope of a family of light rays reflected from
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
reflecting the vertical rays
is the catenary
.
As of this snapshot date, this entry was owned by pahio.