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 side with the corresponding letter) is strictly less than a straight angle. The difference between the measure of a straight angle and the sum of the measures of a triangle's angles is called the defect of the triangle. The area of a hyperbolic triangle is equal to its defect multiplied by the square of : This theorem, first proven by Johann Heinrich Lambert, is related to Girard's theorem in spherical geometry. In all the formulas stated below the sides , , and must be measured in absolute length, a unit so that the Gaussian curvature of the plane is −1.