Ultimate fate of the universe 7.5 billion years after the Big Bang, that the expansion rate of the universe has likely been increasing, commensurate with the Open Universe theory. However, other recent measurements by Wilkinson Microwave Anisotropy Probe suggest that the universe is either flat or very close to flat. If formula_5, then the geometry of space is closed like the surface of a sphere. The sum of the angles of a triangle exceeds 180 degrees and there are no parallel lines; all lines eventually meet. The geometry of the universe is, at least on a very large scale, elliptic. In a closed universe, gravity
Schwarz triangle function case the region in the sector between the radii "OA" and "OB" outside the edge "AB" is convex as the intersection of three convex regions. By induction the angles at "A" and "B" are greater than or equal to /3. Thus the geodesics to "C" from "A" and "B" start off in the region; by convexity, the triangle "ABC" lies wholly inside the region. The quadrilateral "OACB" has all its angles less than (since "OAB" is a geodesic triangle), so is convex. Hence the radius "OC" lies inside the angle of the triangle "ABC" near "C". Thus the angles between