![]() ![]() ③ Line segments (arcs of great circles) have bounded length, and regions on the surface of the sphere have bounded area. ② Angles in a triangle (each side of which is an arc of a great circle) add up to more than \(180\) degrees. In fact, all great circles intersect in two antipodal points. ① There are no parallel lines in spherical geometry. However, it differs from typical Euclidean geometry in several substantial ways: For instance, a "line" between two points on a sphere is actually a great circle of the sphere, which is also the projection of a line in three-dimensional space onto the sphere. Spherical geometry works similarly to Euclidean geometry in that there still exist points, lines, and angles. Spherical geometry is the study of geometric objects located on the surface of a sphere.
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