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.