Discuss the ratio of circumference to diameter for circles on the sphere. the Euclidean radius is...

Discuss the ratio of circumference to diameter for circles on the sphere.

the Euclidean radius is the distance to the (Euclidean) center of the circle -- which
is not a point on the sphere. But the circle also has a center on the
sphere -- this would be the North (or South) Pole for lines of
latitude. So the spherical radius of such a circle is different, namely
the spherical distance from the (spherical) center.

Derive formulas relating these various notions of radius and circumference.

Expert Solution

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Colby Messinger answered 8 months ago

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