A right triangular plate scaled by a factor two generates a bigger plate composed of four triangular plates the same size as the original. By using dimensional analysis we write the moment of inertia ...

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 area moment of inertia (also called the second moment of area) defines the resistance of a cross-section to bending, due to the shape of the cross-section. It is a key parameter for the analysis ...

Nernst's theorem—a general experimental observation presented in 1905 that entropy exchanges tend to zero when the temperature tends to zero—has been directly linked to the second principle of ...

A Greenfoot template that enhances collision detection using convex hulls and the Separating Axis Theorem, optimized with an efficient hybrid approach.

Automating mathematical reasoning has long been a goal in artificial intelligence, with formal frameworks like Lean 4, Isabelle, and Coq playing a significant role. These frameworks enable users to ...