If the side lengths of a triangle form a geometric progression and are in the ratio 1 : "r" : "r"2, where "r" is the common ratio, then "r" must lie in the range −1 < "r" < , which is a consequence of the triangle inequality (the sum of any two sides of a triangle must be strictly bigger than the length of the third side). If "r" = then the shorter two sides are 1 and but their sum is 2, thus "r" < . A similar calculation shows that "r" > −1. A triangle whose sides are in the ratio 1 : : is a right triangle (because 1 + = 2) known as a Kepler triangle.