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
Divergence of the sum of the reciprocals of the primes induction: The first partial sum is , which has the form . If the th partial sum (for ) has the form , then the st sum is as the st prime is odd; since this sum also has an form, this partial sum cannot be an integer (because 2 divides the denominator but not the numerator), and the induction continues. Another proof rewrites the expression for the sum of the first reciprocals of primes (or indeed the sum of the reciprocals of "any" set of primes) in terms of the least common denominator, which is the product of all