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What is the name for I can only describe as the circumference of a sphere. I mean like the equator on a planet. What is the line called which goes around the entire sphere, it can be anywhere (so not just in the middle of the top and the bottom, if your talking about a planet or something) and the length of it equals 2πr.

Another way to describe it is if you put a plane through sphere at any angle so that 2 equal halves are created, what is the name of the line where the plane intersect the sphere's surface.

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up vote 7 down vote accepted

A "great circle", so called because they are the largest possible circles on a sphere. If you're on a sphere (say, Earth) and you want to go between two points using the shortest path, then a great circle is the path you should follow. This makes them like straight lines for spheres.

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Or in technical terms, arcs of great circles are geodesics. –  J. M. Oct 30 '10 at 11:15

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