Spherical geometry other geometric concepts are defined as in plane geometry, but with straight lines replaced by great circles. Thus, in spherical geometry, angles are defined between great circles, resulting in a spherical trigonometry that differs from ordinary trigonometry in many respects; for example, the sum of the interior angles of a triangle exceeds 180 degrees. Spherical geometry is "not" elliptic geometry, but is rather a "subset" of elliptic geometry. For example, it shares with that geometry the property that a line has no parallels through a given point. Contrast this with Euclidean geometry, in which a line has one parallel through
Circular surface "I" → R is called the base curve for the circular surface and the two maps u, v : "I" → R are called the direction frame for the circular surface. For a fixed "t" ∈ "I" the image of "ƒ"("t", "θ") is called a generating circle of the circular surface. Circular surfaces are an analogue of ruled surfaces. In the case of circular surfaces the generators are circles; called the generating circles. In the case of ruled surface the generators are straight lines; called rulings. Circular surface In mathematics and, in particular, differential geometry a circular surface is the