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 Pythagorean theorem is crucial in various fields, including construction, manufacturing and navigation, enabling precise measurements and the creation of right angles for large structures. It ...

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 ...

British professor Sir Andrew Wiles was awarded mathematics’ most prestigious prize this week, for providing the proof to a theorem that had stymied everyone in the field for over 350 years. Wiles was ...

Pythagoras' theorem close Pythagoras' theoremPythagoras's theorem applies to right-angled triangles. The area of the square drawn on the hypotenuse is equal to the sum of the squares drawn on the ...

Observing, gathering knowledge and making predictions are the foundations of the scientific process. The accuracy of our predictions depends on the quality of our present knowledge and accuracy of our ...