Brahmagupta's Formula

The Indian mathematician Brahmagupta published a remarkable formula in his 628 CE treatise Brahmasphutasiddhanta: the area of any quadrilateral inscribed in a circle equals √((s−a)(s−b)(s−c)(s−d)), where a, b, c, d are the side lengths and s is the semiperimeter. When one side is zero, this reduces to Heron's formula for triangles. Brahmagupta also gave the first systematic treatment of zero and negative numbers as mathematical quantities — concepts so fundamental we can barely imagine mathematics without them.