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
Sagitta (geometry) Sagitta (geometry) In geometry, the sagitta (sometimes abbreviated as sag) of a circular arc is the distance from the center of the arc to the center of its base. It is used extensively in architecture when calculating the arc necessary to span a certain height and distance and also in optics where it is used to find the depth of a spherical mirror or lens. The name comes directly from Latin "sagitta", meaning an arrow. In the following equations, denotes the sagitta (the depth of the arc), equals the radius of the circle, and half the length of the chord