type algebra

An animated introduction to geometric algebra, presented as a language that can describe most of physics. It was made with manim and covers multivectors and how they generalize familiar tools like cross products and quaternions.

Professor Brailsford of the University of Nottingham describes how the university set out to print its own mathematics exam papers in the 1980s. The story centers on getting a Mergenthaler Linotron 202 typesetter to work with their own software.

3Blue1Brown's chapter on eigenvectors and eigenvalues in the Essence of Linear Algebra series. It builds a visual intuition for what they mean, why an eigenbasis is useful, and ends with a puzzle.

Bill Hammack of engineerguy uses slow motion video to show how the IBM Selectric typewriter works. He focuses on its fully mechanical digital-to-analog converter, which turns key presses into rotation of the type ball.

A 10-minute 3Blue1Brown chapter explaining the determinant as the factor by which a linear transformation scales area or volume. It builds the idea geometrically with animations before any formulas.

Matt Parker talks Numberphile through the different kinds of numbers: algebraic, transcendental, computable, normal, and beyond. It shows how few numbers we can actually name or describe.

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.

3Blue1Brown, in collaboration with minutephysics, introduces the math of superposition and quantum states using polarized light. It builds up the quantum behavior of photons as a simple counting and probability problem.

3Blue1Brown introduces group theory and abstract groups, then builds toward classification of finite simple groups and the enormous Monster group with its 196,883 dimensions.

A three-minute excerpt from Milton Friedman's Free to Choose in which he uses a pencil to show that no single person knows how to make it. He argues that the free market coordinates countless strangers peacefully.

Practical Engineering's explanation of the February 2021 Texas winter storm and the resulting power grid outage. It lays out the facts about ERCOT, the grid's isolation, and how generation across fuel types failed in the cold.

Everyday Astronaut's Tim Dodd runs an hour-long, data-driven analysis of what rockets actually emit and how that compares with airliners and other industries. It breaks down exhaust by propellant type, per-passenger and total emissions, and ways launches could be cleaner.

Everyday Astronaut explains the basic physics of rocket engines, the main engine cycles and fuel types, then compares SpaceX's methane-fueled full-flow staged combustion Raptor to other engines. It runs nearly 50 minutes with chapter markers.

Technology Connections explains why humidity matters and compares the main types of humidifiers, including evaporative and ultrasonic designs. It covers how and why you would add moisture to indoor air.

Numberphile's James Grime introduces quaternions, a type of number beyond the complex numbers, building up from real and complex numbers and explaining why they are useful.

Technology Connections explains why the superheterodyne radio has its name and how mixing frequencies lets it tune stations well. It walks through the underlying wave phenomena and algebra and why the design solved a hard tuning problem.

Aaron Francis walks through how PHP has changed from 2012 to 2023, covering traits, array destructuring, generators, typed properties and more. It is a quick chaptered tour of modern PHP features.

ACS Reactions investigates why Mexican Coke, supposedly cane sugar sweetened, tested as having glucose and fructose, explaining that sucrose breaks down in acidic soda.

Veritasium visits the US Navy's Crane facility to test top night vision goggles. It explains how image intensifier tubes and thermal or digital systems work and compares the generations of the technology.

Wendover Productions explains why American towns, retail and buildings increasingly look alike, covering zoning pressures, corporate standardization and cheap construction types like 5-over-1 buildings.