Bhaskaracharya Pratishthana
is pleased to announce a guest lecture by
Prof. Prithwijit De, National Coordinator,
Mathematical Olympiad Programme
Details of the Lectures:
- Day and Date: Monday, 10th November 2025
- Timing: 4:00 PM
- Speaker: Prof. Prithwijit De
- Venue: Audio – Visual Hall, Library Building, Bhaskaracharya Pratishthana, Pune.
- Title: On Brahmagupta’s , Kummer’s and Newton’s Quadrilaterals
Abstract:
Unlike the Greeks who developed geometry as a deductive science, the Indians were interested in its arithmetic aspects from early times. For instance, the 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 existence and construction of cyclic quadrilaterals whose sides and diagonals are rational. Later, the German mathematician, Ernst Kummer, made a critical study of the original work of Brahmagupta and showed that the existence of rational quadrilaterals (not necessarily cyclic) is equivalent to the existence of rational points of a particular type on certain cubic curves. We will briefly discuss Brahmagupta’s and Kummer’s methods of construction of rational (cyclic) quadrilaterals.
In his 1720 algebra textbook Universal Arithmetik, Isaac Newton included a section entitled “How geometrical questions may be reduced to equations.” One of the problems he treated was that of finding the diameter of a circle having an inscribed convex quadrilateral, three of whose side lengths a,b,c are given, while the d is a diameter. This problem led him to a relation known as Newton’s equation . Over the years it attracted the attention of many mathematicians who were interested in finding out all its rational solutions. We will present a couple of methods of finding the rational solutions of Newton’s equations.
All are cordially invited to attend the lecture.