differential geometry

Rick Hartley's AltiumLive keynote on differential pairs in PC boards. He argues the rules from cables and twisted pairs do not carry over, and covers which pair geometry gives the best impedance control, the right spacing, routing practice and how much skew is acceptable.

A 1937 GM-produced film explaining how the automobile differential lets wheels turn at different speeds around a corner. It uses clear animations and cutaway demonstrations to build the idea from first principles.

A 1930s Chevrolet training film explaining the principles and development of the differential gear. It builds the idea step by step from first principles to the finished mechanism.

CodeParade's short devlog on how spherical geometry looks in 2D and 3D and why it feels so unusual, part of the Hyperbolica series on a non-Euclidean game.

Andres Gomez Emilsson of the Qualia Research Institute presents a model of DMT experiences using hyperbolic geometry and dynamical systems theory. He describes how different intoxication levels correspond to changing curvature and information content of experience.

The Plasticity creator explains what a geometry kernel is and compares commercial options C3D, ACIS, and Parasolid, describing his months of research and why he chose as he did.

Brian Karis's SIGGRAPH 2021 talk explains how Unreal Engine 5's Nanite virtualized geometry works. It covers mesh import, the data structures, streaming, decompression, culling, software and hardware rasterization, and shading.

Neil Fraser of Google presents Differential Synchronization, the algorithm behind MobWrite, for keeping multiple copies of a document in sync in real time. The talk argues the approach is robust, convergent and efficient.

The first of an eight-part ScienceClic series building general relativity, covering worldlines, proper time and coordinate systems with animated visualizations.

minutephysics, in collaboration with the US Census Bureau, explains differential privacy and why the 2020 census adds noise to protect individuals' data. It walks through how statistics can leak private information.

Henry Segerman and collaborators demonstrate virtual reality experiences in non-Euclidean spaces, including hyperbolic and mixed hyperbolic-Euclidean geometry. The browser-based demos let viewers move through these spaces and show how strange the geometry feels from inside.

Matt Parker on Numberphile explains the strange properties of spheres in higher dimensions, such as how they poke out of their bounding boxes. It uses Pythagoras to build intuition for 4D and beyond.

A 1953 US Navy training film on the basic mechanisms in fire control computers: shafts, gears, cams and differentials. It shows how these mechanical parts compute ship and target firing solutions.

PBS Space Time explains how spacetime geometry and light cones determine the order of events and what can cause what. It visualizes causality in special relativity.

A short video illustrating the hazard of pressure differentials (delta P) in commercial diving, where a pressure difference creates enormous force on a diver. It is a safety-oriented look at diving accidents.

3Blue1Brown visualizes high-dimensional spheres to explain a surprising puzzle about how a sphere fits in a box as dimensions grow. It builds geometric intuition for counterintuitive properties of high-dimensional space.

Donald Knuth's 2017 Christmas Tree Lecture at Stanford about a combinatorial geometry problem whose computed numbers matched a striking formula. He tells the story of the conjecture and its sequel.

Richard Hamming's 1995 lecture on n-dimensional space, showing how geometric intuition about spheres and cubes breaks down in high dimensions. It is part of his course on learning to learn.

The old announcement trailer for Hyperbolica, CodeParade's Unity game set in hyperbolic and spherical space. The creator has since posted devlog videos on building it.

A Sesame Street animation from 1979 with music composed by Philip Glass, showing geometric circle patterns.

3Blue1Brown presents Bayes' theorem through a geometric diagram, showing how evidence should update beliefs. It works through the Kahneman and Tversky style questions and base rates.

Numberphile talks with Grant Sanderson of 3Blue1Brown about a darts puzzle with a shrinking bullseye. Solving it takes the volumes of high-dimensional spheres, and the answer turns up Euler's number.

The first lecture of N J Wildberger's History of Mathematics course, starting with Pythagoras' theorem and following Stillwell's text. It emphasizes the flow of ideas over proofs.

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.

A short clip from Carl Sagan's Cosmos in which he explains how Eratosthenes measured the circumference of the Earth using shadows in two Egyptian cities. It is a clear, visual account of an ancient scientific feat.

Mathologer shows how times table diagrams on a circle produce cardioids and other curves connected to the Mandelbrot set. He explains the patterns and links to a tool for making your own diagrams.

Matt Parker gives a hands-on Royal Institution talk on how four-dimensional shapes appear in a 3D world, with props like straw frames, Mobius strips and a knitted hat. It is a playful general-audience tour of the fourth dimension.

A segment from Carl Sagan's original Cosmos explaining the fourth spatial dimension through analogy with a two-dimensional world and shadow projection.

A CGP Grey video about why pentagons are bad at tiling and why hexagons are so special, in his usual playful style. It touches on honeycombs and tiling in nature.

Numberphile interviews Grant Sanderson of 3blue1brown about Bertrand's paradox, where different reasonable ways of picking a random chord of a circle give different probabilities.

A short explainer showing what walking through walls would look like with movement in a fourth spatial dimension, using the 4D puzzle game Miegakure.

A one-minute clip of Alexander Overwijk drawing a near-perfect freehand circle, one metre across, in under a second on a chalkboard. He is a repeat winner of the World Freehand Circle Drawing Championship.

A talk by Eric Weinstein on gauge theory and its possible application to economics and inflation. It proposes extending the Wu-Yang dictionary into a geometric tool beyond physics.

A 21-minute animation showing how a sphere can be turned inside out without creases or tears, known as sphere eversion.

The first lecture of Gilbert Strang's MIT 18.06 Linear Algebra course, covering the geometry of linear equations. It opens a full 35-lecture university course.

A 1953 US Navy training film explaining the basic mechanisms in mechanical fire control computers aboard ships. It shows how gears, differentials and cams solved mathematical problems in permanent mechanical form.

The first video of 3Blue1Brown's Essence of Calculus series, which builds toward integrals, derivatives, and the fundamental theorem of calculus from a simple geometry question. It aims to make viewers feel they could have invented calculus themselves.

Bisqwit builds a Doom or Duke Nukem 3D style software-rendered 3D engine in C from scratch, supporting non-Euclidean geometry. It covers vector rotation and portal rendering with sped-up, tool-assisted coding.

Veritasium tells the history of how imaginary numbers arose from the quest for a general solution to the cubic equation, including the duels and secrecy among Renaissance mathematicians. It argues math had to give up the requirement that it mirror reality.

The first part of the ending alien sequence from the 2018 film Annihilation, with its distinctive soundtrack. The scene features a strange, shifting mimic and a surreal visual climax.