geometry

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.

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.

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.

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.

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.

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.

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.

3Blue1Brown's animated visual introduction to the Fourier Transform, showing how a signal breaks into frequency components.

3Blue1Brown walks through a very hard Putnam competition problem and its elegant solution, emphasizing the visual intuition and the thought process behind solving it.

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.

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.

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.

3Blue1Brown explores infinite sums from convergent to divergent, with an introduction to the 2-adic metric, themed on the cycle between discovering and inventing mathematics.

A Veritasium video on the logistic map, showing how a simple population equation leads to chaos and bifurcation. It connects the idea to convection, neuron firing and the Mandelbrot set, with interactive animations.

An animated 11-minute tour of the whole field of mathematics as a single map, showing how pure and applied math and their sub-fields relate to each other.

jan Misali presents an humorous but earnest case for counting in base 6 (seximal) instead of base 10 or 12, comparing the arithmetic advantages of each.

3Blue1Brown presents the Triangle of Power, an alternate notation that unifies powers, logarithms and roots in a single triangular symbol. The video shows how the inverse operations relate and how the notation could help.

Numberphile's Ben Sparks shows why the golden ratio is the most irrational number, using seeds, continued fractions and rational approximations. He also explains why plants use it for spacing leaves and seeds.

3Blue1Brown explains space-filling curves and the Hilbert curve, and how infinite mathematical constructions connect to finite, practical approximations. It touches on mapping between dimensions and sensory ideas.

A short 3Blue1Brown video explaining Euler's formula e^(i*pi) = -1 through dynamics, treating velocity as the thing that moves a point to a new position. It builds geometric intuition for why an exponent with i produces rotation.

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.

Numberphile's Tony Padilla and Matt Parker discuss Graham's number, once the largest number used in a mathematical proof, and how enormous it is.

Sabine Hossenfelder asks whether complex numbers are just a convenient tool or necessary in physics. She discusses a recent paper arguing that quantum mechanics cannot be done with real numbers alone.

Numberphile with Dr Holly Krieger shows how the digits of pi surprisingly emerge from the Mandelbrot set. A short, accessible math explainer.

Mathologer uses continued fractions to show why the golden ratio is the most irrational number, comparing it with root 2, e and pi and pointing to where this shows up in nature.

A Numberphile video in which physicists Tony Padilla and Ed Copeland show a seemingly astounding result that 1+2+3+4+... equals -1/12. The argument is informal and has drawn criticism for glossing over what the result actually means.

A Numberphile video with Dr James Grime on Sloane's Gap, the observation that integers in the OEIS are not evenly represented and some numbers are underrepresented. It explains the clusters of 'interesting' numbers.

Numberphile's James Grime discusses highly composite numbers, nicknamed anti-primes, which have more factors than any smaller number, using 5040 as the central example. It touches on Plato and Ramanujan.

Numberphile with Tim Browning on the sum-of-three-cubes problem and why 33 was the lowest unsolved case. The description notes a later solution for 33.

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.