**Cartesian equation: **

(*x* - *b*)^{2}(*x*^{2} + *y*^{2}) - *a*^{2}*x*^{2} = 0

**Polar equation: **

*r* = *a* + *b* sec(*θ*)

**Click below to see one of the Associated curves.**

If your browser can handle JAVA code, click HERE to experiment interactively with this curve and its associated curves.

The name means

Nicomedes was a minor geometer who worked around 180 BC. His main invention was the conchoid ascribed to him by Pappus. It was a favourite with 17 Century mathematicians and could be used, as Nicomedes had intended, to solve the problems of duplicating the cube and trisecting an angle.

Newton said it should be a 'standard' curve.

The conchoid has *x* = *b* as an asymptote and the area between either branch and the asymptote is infinite. The area of the loop is

b√(a^{2}-b^{2}) - 2ablog((a+ √a^{2}-b^{2})/b) +a^{2}cos^{-1}(b/a).

The conchoid was used in the construction of ancient buildings. The vertical section of columns was made in the shape of the loop of the conchoid.

**Other Web sites:**

JOC/EFR/BS January 1997

The URL of this page is:

http://www-history.mcs.st-andrews.ac.uk/Curves/Conchoid.html