Elliptic geometry is a non-Euclidean geometry with positive curvature which replaces the parallel
postulate with the statement "through any point in the plane, there exist
no lines parallel to a given line." In order to
achieve a consistent system, however, the basic axioms of neutral geometry must be
partially modified. Most notably, the axioms of betweenness are no longer sufficient
(essentially because betweenness on a great circle
makes no sense, namely if 
and 
are on a circle and 
is between them, then the relative position of 
is not uniquely specified), and so must be replaced with the
axioms of subsets.
Elliptic geometry is sometimes also called Riemannian geometry. It can be visualized as the surface of a sphere on which "lines"
are taken as great circles. In elliptic geometry,
the sum of angles of a triangle is 
.
