# Circle and Infinity?

by mathlove3.14159
Tags: circle, infinity
 P: 2 Why is it that a circle with an infinitly large radius is a line?
P: 39
 Quote by mathlove3.14159 Why is it that a circle with an infinitly large radius is a line?

Why is it that this planet looks flat to our point of perception?
 P: 608 Depends on your definition of "circle".
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P: 38,706

## Circle and Infinity?

There is no such thing as a "circle with infinite radius". What is true is that the "curvature" of a circle with radius R is 1/R. In the limit, as the radius goes to infinity (which NOT the same as saying the radius is infinite!), the curvature goes to 0 and the only "curve" having curvature 0 at every point is a straight line.

By the way, in hyperbolic geometry, the limit of a sequence of circles, having the same center but increasing radius, is NOT a straight line but a "horocycle".
 P: 608 There is no such thing as a "circle with infinite radius". Depends on your definition of "circle". In complex analysis we sometimes see a definition of "circle" that includes lines. That way it doesn't matter whether we think of the complex numbers as a plane (Argand) or a sphere (Riemann).
 P: 164 A curve is line because as the radius becomes larger, it becomes like a line. Try it in your compass.
P: 244
 Quote by darkmagic A curve is line because as the radius becomes larger, it becomes like a line. Try it in your compass.
And make sure you have a really big compass.
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