Essence of linear algebra - "[Grant Sanderson of 3Blue1Brown (now at Khan Academy) animates] the geometric intuitions underlying linear algebra, making the many matrix and vector operations feel less arbitrary." [more inside]
Compass-and-straightedge construction (aka Euclidean construction) is a method of drawing precise geometric figures using only a compass and a straightedge (like a ruler without the markings). MathOpenRef maintains a catalog of many common constructions, each with an explanatory animation and a proof. This YouTube video demonstrates how to construct almost every polygon that can be constructed using these methods. [more inside]
I want to demonstrate how amazing combinatorial explosion is! Please don't stop me. An animation about numbers that get large. It has a happy ending and possibly even a moral. [more inside]
Understanding e to the pi i - "An intuitive explanation as to why e to the pi i equals -1 without a hint of calculus. This is not your usual Taylor series nonsense." (via via; reddit; previously) [more inside]
Louis Gorenfeld lovingly explores the mathematics and techniques behind early, pseudo-3D games. [more inside]
Every film Pixar has produced has landed in the top fifty highest-grossing animated films of all time. What's their secret? Mathematics. Oh, and 22 Rules of Storytelling. [more inside]
Animation of prime factorization of the integers based on Brent Yorgey's factorization diagrams, described here. [via Data Pointed, previously.]
Pythagasaurus is the fabled Tyrannosaurus practiced in the skills of trigonometry and long division. Apparently he knows all eight numbers. [Via]
This short computer graphics animation presents the regular 120-cell: a four dimensional polytope composed of 120 dodecahedra and also known as the hyperdodecahedron or hecatonicosachoron. [more inside]
Bruce and Katharine Cornwell are primarily known for a series of remarkable animated films on the subject of geometry. Created on the Tektronics 4051 Graphics Terminal, they are brilliant short films, tracing geometric shapes to intriguing music, including the memorable 'Bach meets Third Steam Jazz' musical score in ‘Congruent Triangles.’
How deep does the rabbit hole go? The Ultimate Fractal Video Project features animated zooms into the famous Mandelbrot Set. Some zoom in so far that, by the end of the dive, the first frame you had viewed would be as large as (or larger than) the known universe. | The animations are offered as .zip'd WMV files; lower-quality versions are viewable on FractAlkemist's YouTube page. [more inside]
Flash Animations for Physics. Animations and interactive demos available in many varieties, such as classical mechanics, nuclear, quantum, and relativistic. There's even a nice explanation of the forces at work in Curling. And if that doesn't wet your geek whistle, then take a peek at the patterns of Visual Math.
Simpsonsmath.com: a guide for teachers to engage math-o-phobes with animated fun. "Mmmmmm, pi."