In the paper, the authors present several inequalities for bounding the sums of two sine cardinal functions and the sums of two hyperbolic sine cardinal functions. These inequalities improve ...

This is an updated version of a story first published on May 5, 2024. For many high school students returning to class, it may seem like geometry and trigonometry were created by the Greeks as a form ...

The Pythagorean Theorem—discovered by the Greek mathematician Pythagoras in the 6th century BCE—is a cornerstone of mathematics. Simply stated as a 2 + b 2 = c 2, the theorem posits that the sum of ...

Two US college students, who discovered a new way to prove Pythagoras' famous 2,000-year-old theorem in 2022 have now come up with five different ways of solving the problem using trigonometry. Their ...

Formulae for ζ(2n) and Lχ4 (2n + 1) involving Euler and tangent numbers are derived using the hyperbolic secant probability distribution and its moment generating function. In particular, the Basel ...