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A 180 degree circular arc (i.e. a half sphere) is obvious:

When you rotate this about its two end points, you get a sphere.

What about for something less than 180 degrees (e.g. 90)?:

I believe this forms an ellipsoid, with coefficients a and b being equal, with respect to wikipedia's entry on ellipsoid: http://en.wikipedia.org/wiki/Ellipsoid. Can anyone confirm that is correct?

I have no idea what it would be for something greater than 180 degrees:

Its cross section would look like a butterfly. I have no idea what the 3D shape would be called. Anyone have any idea? I'm especially interested in obtaining an equation that would describe its surface.

When you rotate this about its two end points, you get a sphere.

What about for something less than 180 degrees (e.g. 90)?:

I believe this forms an ellipsoid, with coefficients a and b being equal, with respect to wikipedia's entry on ellipsoid: http://en.wikipedia.org/wiki/Ellipsoid. Can anyone confirm that is correct?

I have no idea what it would be for something greater than 180 degrees:

Its cross section would look like a butterfly. I have no idea what the 3D shape would be called. Anyone have any idea? I'm especially interested in obtaining an equation that would describe its surface.

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