Circles and hyperbolas are, in a sense, surprisingly similar shapes. In this video, we explore the mystery behind their strange connection and step into a world of “rotation” and “angle” with meanings quite different from the usual ones. The key to this story lies in hyperbolic functions, which share many properties with trigonometric functions.

This video was really helpful in understanding the hyperbolic functions! Was happy to see that a connection I saw to spacetime is actually an application of them.

In this video, I present the story of phase space and one of the most fundamental theorems of classical physics — Liouville’s theorem. This is a walk through the birth of phase space and how the discovery of Liouville’s theorem involves not only Liouville but also Jacobi and Boltzmann.