Inversive Geometry I: Basic Properties of Inversion

inversion of a

point

Given a fixed circle (depicted in orange) of center

q

and radius

r

, inversion is a mapping fixing it and swapping its interior and exterior in such a way that the product of the distances to

q

of a point and its image (both in line with

q

) is equal to

2

r

. This Demonstration shows the effect of inversion on points, circles, lines, circles passing through

q

, vertices of triangles and squares, and the interior of triangles. Handles are provided (in red double circles) to let you vary these shapes.