Strophoids
- Author:
- Steve Phelps
Let S be any curve and O a point (called the pole) and a fixed point A. If a variable line through O meets curve S at Q, and points P and P' are on this line such that
P'Q = QP = QA
the locus of P and P' is called the strophoid of S with respect to the pole O and the fixed point A.Oblique Strophoid
A strophoid of a line with respect to a pole not on the line and a fixed point on the line.
Right Strophoid
A strophoid of a line with respect to a pole not on the line where the fixed point is the foot of the perpendicular dropped from the pole.
Freeth's Nephroid
The strophoid of a circle with respect to its center as the pole and a fixed point on the circumference.
Other Strophoids
The strophoid of a circle with respect to a point on the circumference, with the fixed point being diametrically opposed to the pole.
The strophoid of a circle with its center as the pole and a fixed point not on the circle.
The strophoid of a parabola with the pole being the vertex and the focus being the fixed point.