We investigate here the representability of integers as sums of triangular numbers, where the n-th triangular number is given by Tn = n(n+1)/2. In particular, we show ...

The textbook uses examples from Indian monuments and cultural contexts to explain key concepts of the subject, including ...

In this triangle \(a^2 = b^2 + c^2\) and angle \(A\) is a right angle. Pythagoras' theorem only works for right-angled triangles, so you can use it to test whether a triangle has a right angle or not.

An understanding of how to use Pythagoras’ theorem to find missing sides in a right-angled triangle is essential for applying the theorem in different contexts. (3,1) is the coordinate that is 3 along ...

The Pythagoras theorem 'should either be an Egyptian theorem if you look at the standard of just having an idea about it, an Indian theorem if you're looking for a complete statement of it, or a ...

Do you think there’s a triangle whose angles measure 41, 76 and 63 degrees? At first, answering this may seem easy. From geometry class we know that the sum of the measures of the interior angles of a ...

Let (H, R) be a triangular Hopf algebra and let V be a finite-dimensional representation of H. Following Manin we imitate the standard algebraic constructions in order to define the relativized ...