On Brahmagupta's and Kummer's quadrilaterals

Abstract

The Greeks developed geometry as a deductive science, its main results being derived from axioms. The Indians, however, studied geometry in its arithmetic aspects from early times. For instance, construction of right angled triangles with rational sides and hypotenuse was a problem of interest right from the Sulva period in India. In this tradition, Brahmagupta, in the 7th century AD, studied the question of the existence and construction of (cyclic) quadrilaterals whose sides and diagonals are rational. This work came to light to the European mathematicians through the work of Colebrooke [2]. Chasles, the French geometer, was so fascinated by this that he, in fact, included a note on Brahmagupta’s work in [1].