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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.
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