What is "strophoid"

n. (context geometry English) A certain kind of curve.

In geometry, a strophoid is a curve generated from a given curve C and points A (the fixed point) and O (the pole) as follows: Let L be a variable line passing through O and intersecting C at K. Now let P and P be the two points on L whose distance from K is the same as the distance from A to K. The locus of such points P and P is then the strophoid of C with respect to the pole O and fixed point A. Note that AP and AP are at right angles in this construction.

In the special case where C is a line, A lies on C, and O is not on C, then the curve is called an oblique strophoid. If, in addition, OA is perpendicular to C then the curve is called a right strophoid, or simply strophoid by some authors. The right strophoid is also called the logocyclic curve or foliate.