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
Hyperbolic triangle relations between the sides "s" and the angles "A" of an equilateral triangle (a triangle where all sides have the same length and all angles are equal). The relations are: Whether "C" is a right angle or not, the following relationships hold: The hyperbolic law of cosines is as follows: Its dual theorem is There is also a "law of sines": and a four-parts formula: For hyperbolic trigonometry: Hyperbolic triangle In hyperbolic geometry, a hyperbolic triangle is a triangle in the hyperbolic plane. It consists of three line segments called "sides" or "edges" and three points called "angles" or "vertices".