Circle Inversion of Basic Figures

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Explore the circle inversion of six figures. Drag the locators to move and scale the red pre-image. The blue shape is the image after circle inversion in the dashed circle.
Contributed by: Garrett Nelson (June 2014)
Suggested by: Branko Curgus
Open content licensed under CC BY-NC-SA
Snapshots
Details
Inversion of a point in a circle
with center
and radius
to a point
is the nonlinear mapping of the plane (except for the point
) to itself defined by
, where
,
, and
are collinear. Inversion swaps the interior and exterior of
, preserves angles, and maps generalized circles to generalized circles. (A generalized circle is either an ordinary circle or a straight line.)
Permanent Citation
"Circle Inversion of Basic Figures"
http://demonstrations.wolfram.com/CircleInversionOfBasicFigures/
Wolfram Demonstrations Project
Published: June 30 2014