#
Spherical/Elliptical Geometry

Spherical geometry replaces the standard flat plan with the plane
being the surface of a sphere. Lines are defined as "great circles"
of the sphere. A great circle is determined by taking the plane
including any two points on the surface of the sphere and the center
of the sphere and intersecting that plane with the surface of the
sphere. If you visualize the plane as the globe, then lines of
latitude are not great circles (except for the equator), and lines of
longitude are. Elliptical Geometry takes the spherical plan and
removes one of two points directly opposite each other. The end
result is that in spherical geometry, lines always intersect in
exactly two points, whereas in elliptical geometry, lines always intersect in one point.

## Properties of Elliptical/Spherical Geometry

In Spherical Geometry, all lines intersect in 2 points. In elliptical geometry, lines intersect in 1 point. In addition, the angles of a triangle always add up to be greater than 180 degrees. In elliptical/spherical geometry, all of Euclid's postulates still do hold, with the exception of the fifth postulate. This type of geometry is especially useful in describing the Earth's surface.

## But is it really Non-Euclidean?

There is some debate as to wether spherical and elliptical
geometries are actually strictly non-Euclidean. The particular areas
of contention concern wether, because lines on a sphere loop back over
each other, they are actually infinte. However, the "end" is never
actually reached, which makes some consider it infinite.