Equilateral pentagon of δ can be seen from the figure: Simplifying, δ is obtained as function of α and β: The remaining angles of the pentagon can be found geometrically: The remaining angles of the orange and blue triangles are readily found by noting that two angles of an isosceles triangle are equal while all three angles sum to 180°. Then formula_7 and the two remaining angles of the green triangle can be found from four equations stating that the sum of the angles of the pentagon is 540°, the sum of the angles of the green triangle is 180°, the angle
Divergence of the sum of the reciprocals of the primes these primes. Then each of these primes divides all but one of the numerator terms and hence does not divide the numerator itself; but each prime "does" divide the denominator. Thus the expression is irreducible and is non-integer. Divergence of the sum of the reciprocals of the primes The sum of the reciprocals of all prime numbers diverges; that is: This was proved by Leonhard Euler in 1737, and strengthens Euclid's 3rd-century-BC result that there are infinitely many prime numbers. There are a variety of proofs of Euler's result, including a lower bound for the partial sums stating that for