I have very fond memories of high school geometry. Memorizing theorems wasn't too hard, and solving proofs was like solving the logic puzzles that I did for fun anyway. But the theorems were scattered ...

Mathematics is distinguished from the sciences by the freedom it enjoys in choosing basic assumptions from which consequences can be deduced by applying the laws of logic. We call the basic ...

The Pythagorean Theorem, a cornerstone of geometry, empowers students to solve right triangle problems and unlock advanced mathematical concepts. Mastering this theorem enhances logical reasoning, ...

Napoleon Bonaparte, First Consul. Work by Ingres. It was during this period that he came into contact with the theorems. Credit: Public domain / Wikimedia Commons His political stance allowed him to ...

We review some results and open problems for harmonic measure. Their common element is their simple geometric character. Such classical results are the projection estimates of Beurling, Nevanlinna and ...

This article presents a way of studying the rationality that mathematics teachers utilize in managing the teaching of theorems in high-school geometry. More generally, the study illustrates how to ...

The Pythagorean theorem, a cornerstone of mathematics for millennia, provides a method for determining unknown sides in right-angled triangles using the formula a² + b² = c². Its applications extend ...

To illustrate the Pythagorean Theorem, makers of geometric models have long made models with pieces that could be arranged either as a square with a side equal to the length of the hypotenuse of a ...

Stochastic processes form the backbone of modern probability theory, describing systems that evolve randomly over time or space. They are instrumental in areas ranging from statistical physics to ...