Riemannian geometry is a non-Euclidean geometry. It can be visualized as taking place on the surface of a sphere. In Riemannian geometry, lines are the great circles on the sphere. As a consequence, every pair of distinct lines intersect in Riemannian geometry. The points of intersection are antipodal, are diametrically opposed.
Riemannian geometry is also called Elliptic Geometry.
Click on the blue points in manipulative 1 and drag them to change the figure. Notice that two distinct great circles always intersect.
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