Euclidean geometry is only an approximate description of the earth’s surface, for example, and this is why flat maps always entail distortions of the actual shapes. The distortions might be negligible...Euclidean geometry is only an approximate description of the earth’s surface, for example, and this is why flat maps always entail distortions of the actual shapes. The distortions might be negligible on a map of Connecticut, but severe for a map of the whole world. That is, the globe is only locally Euclidean. On a spherical surface, the appropriate object to play the role of a “line” is a great circle. The lines of longitude are examples of great circles.
