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 ...

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 most important theorem we learnt in childhood carries the name of a Greek philosopher, but not necessarily the legacy.

Two years ago, a couple of high school classmates each composed a mathematical marvel, a trigonometric proof of the Pythagorean theorem. Now, they’re unveiling 10 more. For over 2,000 years, such ...

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 ...

Mathematics students frequently encounter challenges when tackling geometric concepts, especially those requiring spatial visualisation skills. The transition from basic arithmetic to geometric ...

Hundreds of years before a Greek scholar outlined his proof of the Pythagorean theorem, ancient Chinese scholars proved it using just 17 characters, a renowned Chinese mathematician highlighted in a ...