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 ...

Pythagoras’ theorem is a statement that is true for all right-angled triangles.It states that the area of the square on the hypotenuse close hypotenuseThe longest side of a right-angled triangle, ...

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

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 ...

On November 26, 1949, Albert Einstein published an essay in the Saturday Review of Literature in which he described two pivotal moments in his childhood. The first involved a compass that his father ...

Do you remember the Pythagoras Theorem, which you once studied in Mathematics, was a discovery of Pythagoras? In today’s time, people often wonder when Pythagoras was born, his full name, and his ...

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 ...

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.

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 ...

In a new peer-reviewed study, Ne'Kiya Jackson and Calcea Johnson outlined 10 ways to solve the Pythagorean theorem using trigonometry, including a proof they discovered in high school. When you ...