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 ...

The earliest known evidence for the Pythagorean Theorem comes from an ancient clay tablet called, “IM 67118.” This tablet uses the theorem to determine the length of a diagonal within a rectangle, and ...

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 ...

A classical theorem of MacMahon states that the number of lozenge tilings of any centrally symmetric hexagon drawn on the triangular lattice is given by a beautifully simple product formula. In this ...

Abstract: The universal approximation capability of type-2 fuzzy neural networks plays an important role in the approximation theory of type-2 fuzzy neural networks. In this study, we propose 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 ...