Editing Parallel (geometry) (section)

=== Spherical or elliptic geometry ===
{{See also| Spherical geometry|Elliptic geometry}}

[[File:SphereParallel.png|thumb|300px|right|On the [[sphere]] there is no such thing as a parallel line. Line ''a'' is a [[great circle]], the equivalent of a straight line in spherical geometry. Line ''c'' is equidistant to line ''a'' but is not a great circle. It is a parallel of latitude. Line ''b'' is another geodesic which intersects ''a'' in two antipodal points. They share two common perpendiculars (one shown in blue).]]

In [[spherical geometry]], all geodesics are [[great circles]]. Great circles divide the sphere in two equal [[Sphere|hemispheres]] and all great circles intersect each other. Thus, there are no parallel geodesics to a given geodesic, as all geodesics intersect. Equidistant curves on the sphere are called '''parallels of latitude''' analogous to the [[latitude]] lines on a globe. Parallels of latitude can be generated by the intersection of the sphere with a plane parallel to a plane through the center of the sphere.
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