midpoint is the two points that mark the end of an arc.
midpoint is the two points that mark the end of an arc.
the two points that mark the end of an arc?
midpoint
in spherical geometry, the shortest distance between two points is an arc of a great circle, but the triangle inequality holds provided the restriction is made that the distance between two points on a sphere is the length of a minor spherical line segment (that is, one with central angle in ) with those endpoints.
triangle inequality
the length of the line-segment is the shortest length between two points. the arc-length of a hypercycle connecting two points is longer than that of the line segment and shorter than that of a horocycle, connecting the same two points. the arclength of both horocycles connecting two points are equal. the arc-length of a circle between two points is larger the arc-length of a horocycle connecting two points.









































if the gaussian curvature of the plane is −1 then the geodesic curvature of a horocycle is "1" and of a hypercycle is between "0" and "1".









































section::::properties.:triangles.
hyperbolic geometry