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.

The physics and math of spin-1/2 particles: how states of a spin-1/2 correspond to points on a sphere.

Einstein realized that gravity is due to the curvature of spacetime, but let’s go back earlier

Fascinating. Also another great example of how Nature used to be awesome.

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.

Ben Sparks uses simulations for a new insight into Möbius loops.

Very nice video demonstating the power of using the computer when doing mathematics.

see: https://www.geogebra.org/m/v5z33vth

I’ve been thinking about very similar ideas for the better part of a year now; excited to see there’s good work regarding this.

This video is my take on 3B1B’s Summer of Math Exposition (SoME) competition

It explains in pretty intuitive terms how ideas from topology (or “rubber geometry”) can be used in neuroscience, to help us understand the way information is embedded in high-dimensional representations inside neural circuits

In this cross-over episode between the Main Sequence and Tom Academy, we see what it would take to prove that you can’t do what you already thought you couldn’t do, and learn about Tom’s prurient interest in Platonic horrors. Yes, the whole 80 minutes is about cubes and their relatives.

Beautiful weaving of geometry, group theory, and visual art.

When bad news gets me down, I often get insomnia. I wake up in the middle of the night, start thinking about how we’re all doomed, and can’t easily stop. To break out of these doom loops, I do elaborate visualization exercises. They don’t really put me to sleep, they just calm me down…

Lightly depressing nerd shit.

Great series of lectures so far on differential geometry—both discrete and smooth—with a focus on computation. This was a nice reintroduction to topology from another perspective, and I think I’m starting to understand what a manifold is. Probably need to watch it again. :)

It’s a primary school homework question which causes disagreement among seasoned mathematicians.

Great discussion of geometry, semantics, and argumentation stemming from what otherwise feels like an obvious question.

Tendril perversion is a geometric phenomenon sometimes observed in helical structures in which the direction of the helix transitions between left-handed and right-handed. Such a reversal of chirality is commonly seen in helical plant tendrils and telephone handset cords.