... v2v, 2u,u2+ v2v and u2− w2w, 2u,u2+ w2wfor some rational v and w. Putting the two together (Figure 5.2) gives an ar-bitrary rational triangle, and its sides and altitude are of ... 6.3), and a remarkable formula for the area of a cyclic quadrilateral.The latter states that if a quadrilateral has sides a, b, c,andd, semiperimeters, and all vertices on a circle, then its ... Biographical Notes: Brahmagupta and Bhˆaskara 85mathematician named Paul Halcke found a box with rational sides and facediagonals in 1719. Its sides are 44, 240, and 117. However, the bodydiagonal...