Strophoid
In geometry, a
strophoid is a curve generated from a given curve
C and points
A and
O as follows: Let
L be a variable line passing through
O and intersecting
C at
K. Now let
P1 and
P2 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
P1 and
P2 is then the strophoid of C with respect to the pole
O and fixed point
A. Note that
AP1 and
AP2 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.