Monday, April 21, 2014

An infinite circle is a straight line

This is how the Universe works.

A circle with infinite radius is a line

The edge of a circle with infinite radius is straight

"In geometry, inversive geometry is the study of those properties of figures that are preserved by a generalization of a type of transformation of the Euclidean plane, called inversion. These transformations preserve angles and map generalized circles into generalized circles, where a generalized circle means either a circle or a line (loosely speaking, a circle with infinite radius). Many difficult problems in geometry become much more tractable when an inversion is applied. "


"A regular apeirogon has equal-length sides and equal corner angles, just like any regular polygon. Its Schläfli symbol is {∞}.

If the corner angles are 180°, the overall form of the apeirogon resembles a straight line, This line may be considered as a circle of infinite radius, by analogy with regular polygons with great number of edges, which resemble a circle."

Numberphile video "Epic Circles"

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