## Monday, April 21, 2014

### An infinite circle is a straight line

This is how the Universe works.

Links:

http://math.stackexchange.com/questions/82220/a-circle-with-infinite-radius-is-a-linehttp:
A circle with infinite radius is a line

The edge of a circle with infinite radius is straight
http://www.askamathematician.com/2011/04/q-is-the-edge-of-a-circle-with-an-infinite-radius-curved-or-straight/

http://en.wikipedia.org/wiki/Inversive_geometry

"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. "

Apeirogons
http://en.wikipedia.org/wiki/Apeirogon#Regular_apeirogons

"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"
https://www.youtube.com/watch?v=sG_6nlMZ8f4