circle inversion | sphere inverse | sphere inversion

Inversion is the process of transforming points P to a corresponding set of points P' known as their inverse points. Two points P and P' are said to be inverses with respect to an inversion circle having inversion center O = (x_0, y_0) and inversion radius k if P' is the perpendicular foot of the altitude of Δ O Q P, where Q is a point on the circle such that O Q⊥P Q. The analogous notation of inversion can be performed in three-dimensional space with respect to an inversion sphere.

arbelos | circle power | conformal mapping | cyclide | hexlet | inverse curve | inverse points | inversion circle | inversion operation | inversion pole | inversion radius | inversion sphere | inversive distance | inversive geometry | limiting point | midcircle | Pappus chain | Peaucellier inversor | permutation inversion | polar | radical line | Steiner chain | Steiner's porism