**Cartesian equation: **

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

**Polar equation: **

*r* = *a* + *b* sec(*θ*)

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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

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JOC/EFR/BS January 1997

The URL of this page is:

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