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
Incidence (geometry) Incidence (geometry) In geometry, an incidence relation is a heterogeneous relation that captures the idea being expressed when phrases such as "a point "lies on" a line" or "a line is "contained in" a plane" are used. The most basic incidence relation is that between a point, , and a line, , sometimes denoted . If the pair is called a "flag". There are many expressions used in common language to describe incidence (for example, a line "passes through" a point, a point "lies in" a plane, etc.) but the term "incidence" is preferred because it does not have the