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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

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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.)

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