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Originally Posted by CSflim
No, he's not talking about three dimensional geometry, he's talking about two dimensional geometry on a curved surface (e.g. drawing a map of the world on a globe: don't forget, we are talking about the surface of the globe which is 2D, not the actual globe itself, which is 3D). So they would be two-dimensional, just non-euclidean. They are still referred to as "circles", they just don't have the same properties as circles in a euclidean geometry (most pertinently, the fact that c/d does not equal pi).
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Just to amplify this for those unfamiliar with non-Euclidean geometry, surfaces can be defined without embedding them in a higher dimensional space. A sphere for example is a 2-dimensional object. You can define what it means to do geometry on it without ever having to refer to an external space that it might (or might not) be sitting in. The distinction is subtle, but it turns out to be a useful one.