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.

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.

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.

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

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.

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.

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.

Freya Holmer's Dutch Game Day 2023 talk asking why vectors can't be multiplied, building from complex numbers to a single axiom and arriving at geometric algebra, quaternions and multivectors.

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.

Veritasium explains how Penrose tilings and quasicrystals overturned the belief that 5-fold symmetry and non-periodic crystals were impossible, including an interview with Paul Steinhardt.

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.

Owen Maitzen's animated hour-long introduction to Hackenbush, a simple combinatorial game, and how its strategy leads to surreal numbers and the roots of the number system.

Timothy Gowers thinks aloud, in real time, as he tries to understand why Pascal's determinant equals 1. He does not fully solve it in this episode, but shows his exploratory process.

Vsauce asks how many holes a human has and uses topology to show the answer depends on what counts as a hole, with animations and expert input.

A 3Blue1Brown live lockdown math episode asking what Euler's formula e^(pi i) is actually saying. It builds intuition through exponentials, rotation and vectors landing on the unit circle.

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.

Stand-up Maths explains why the perimeter of an ellipse has no simple closed-form equation, showing the infinite series and presenting approximation formulas.

Veritasium explains why no voting system can be perfectly fair, drawing on Arrow's theorem and the work of Eric Maskin. It looks at problems with systems like first-past-the-post and ranked-choice voting.

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.

Marshall Kirk McKusick gives a talk at EuroBSDCon tracing filesystem and storage development from 1979 to today, using the BSD Fast Filesystem as the focus. It covers early disk-geometry optimization through later contiguous layout and small-file performance work.

Epic Games' reveal of Unreal Engine 5, a real-time demo running on PlayStation 5. It showcases Nanite virtualized micropolygon geometry and Lumen global illumination.