Conchoid (mathematics)

A conchoid is a curve derived from a fixed point O, another curve, and a length d. For every line through O that intersects the given curve at A the two points on the line which are d from A are on the conchoid.

The simplest expression uses polar coordinates with O at the origin. If <math>r=\alpha(\theta)<math> expresses the given curve then <math>r=\alpha(\theta)\pm d<math> expresses the conchoid.

All conchoids are cissoids with a circle centered on O as one of the curves.

The prototype of this class is the conchoid of Nicomedes in which the given curve is a line.

A limaçon is a conchoid with a circle as the given curve.

The often-so-called conchoid of de Sluze and conchoid of Dürer do not fit this definition; the former is a strict cissoid and the latter a construction more general yet.