Wednesday, September 17, 2014

Great Circles for an n-sphere

  One can define a great circle on an n-sphere by its intersection with a plane passing through two of its points, a and b, and its center. If the point b isn't perpendicular to the point a one can find the normal by eliminating the a component of b and renormalizing. Here's a proof that the intersection is a unit circle.

A plane that does not pass through the center will have a radius less than unity.

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