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Inverse geometry

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Converse, Inverse, and Contrapositive

In geometry, inversive geometry is the study of inversion, a transformation of the Euclidean plane that maps circles or lines to other circles or lines and that preserves the angles between crossing curves. Many difficult problems in geometry become much more tractable when an inversion is applied. Inversion See more

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Writing the Converse, Inverse, and Contrapositive

The inverse point of ω is the origin; that is, O′ = ω and ω′ = O. So we can create an entirely consistent system of geometry which contains all the points in the Euclidean plane plus a point at infinity which is infinitely far away from every other point. We usually call the Euclidean plane with ω added the extended plane.