Sum of angles of a triangle to zero. For a spherical triangle, the sum of the angles is greater than 180° and can be up to 540°. Specifically, the sum of the angles is where "f" is the fraction of the sphere's area which is enclosed by the triangle. Note that spherical geometry does not satisfy several of Euclid's axioms (including the parallel postulate.) Angles between adjacent sides of a triangle are referred to as "interior" angles in Euclidean and other geometries. "Exterior" angles can be also defined, and the Euclidean triangle postulate can be formulated as the exterior angle theorem. One can also consider the
Hyperbolic triangle scale is most convenient if the lengths are measured in terms of the absolute length (a special unit of length analogous to a relations between distances in spherical geometry). This choice for this length scale makes formulas simpler. In terms of the Poincaré half-plane model absolute length corresponds to the infinitesimal metric formula_1 and in the Poincaré disk model to formula_2. In terms of the (constant and negative) Gaussian curvature of a hyperbolic plane, a unit of absolute length corresponds to a length of In a hyperbolic triangle the sum of the angles "A", "B", "C" (respectively opposite to the