First read the
conchoid writeup. The conchoid of
Nicomedes
is the conchoid associated with the data: a
line, a
point not on the line,
and a
distance.
If we take the line to be x=a, the point to be (0,0)
and the distance to be d then the conchoid has equation:
(x2+y2)(x-a)2=d2x2
Nicomedes used this curve to solve the problem of trisection of the angle,
one of the three geometric problems of antiquity some time around 180 BC.