Given a circle C with center O and radius k, then two points P and Q are inverse with respect to C if O P·O Q = k^2. If P describes a curve C_1, then Q describes a curve C_2 called the inverse of C_1 with respect to the circle C (with inversion center O). The Peaucellier inversor can be used to construct an inverse curve from a given curve. If the polar equation of C is r(θ), then the inverse curve has polar equation r = k^2/(r(θ)).

inversion | inversion center | inversion circle | Peaucellier inversor | reciprocal | reciprocal curve | reciprocation