Inversive Geometry I: Basic Properties of Inversion

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Given a fixed circle (depicted in orange) of center and radius
, inversion is a mapping fixing it and swapping its interior and exterior in such a way that the product of the distances to
of a point and its image (both in line with
) is equal to
. This Demonstration shows the effect of inversion on points, circles, lines, circles passing through
, vertices of triangles and squares, and the interior of triangles. Handles are provided (in red double circles) to let you vary these shapes.
Contributed by: Jaime Rangel-Mondragon (March 2011)
Open content licensed under CC BY-NC-SA
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"Inversive Geometry I: Basic Properties of Inversion"
http://demonstrations.wolfram.com/InversiveGeometryIBasicPropertiesOfInversion/
Wolfram Demonstrations Project
Published: March 7 2011