square knot

A walkthrough of the Quake III fast inverse square root, explaining where the constant 0x5f3759df comes from. It covers IEEE 754 floats, the bit hack that approximates a logarithm, and a Newton's method refinement.

An older 3Blue1Brown video on why topology matters, built around the inscribed rectangle problem. It walks through how tori and Mobius strips appear in the solution. The channel later replaced it with an updated version.

3Blue1Brown shows how pi emerges from prime numbers via complex numbers and sums of squares, culminating in a formula for approximating pi.

Numberphile's Ben Sparks works through the physics of a car crash, showing how kinetic energy grows with the square of speed and why stopping distance climbs so quickly as velocity increases.