This time we'll look at standing wave patterns on hyperspheres — what Hyperspherical Harmonics look like. They are related to possible wave function shapes of 4D atoms (which I plan to explore in deta

This article introduced type theory, which claims to replace set theory's position in mathematics. It has been widely used in machine proofs, most famously in the proof of the Four Color Theorem.

This article summarizes 4D mesh generation algorithms, including pyramid/extrusion/direct product, regular polytopes, orientation processing, and tetrahedral decomposition problems.

Formal systems were proposed to check proofs. I’ll start with simple formal systems then to propositional logic and ZFC set theory. I also built a web-based simulator, which later evolved into a game

Last year CFY suddenly became interested in “googology” and “ordinals”, and even recommended an “ordinal incremental” game Ordinal Markup to me, and then I unfortunately fell into the rabbit hole.

A Soviet cosmonaut was fiddling with a T-shaped object in space when he accidentally discovered that if it was set to float and spin rapidly, its rotation axis would suddenly flip midair. This phenome

This article is a overview of various algorithms for 4D rotation. It covers computational methods for 3D quaternions and 4D rotors, a comparison with Geometric Algebra, as well as various lookAt algor

Previous articles have covered almost all common methods for visualizing 4D: cross-section method, stereographic projection, contour surfaces or color-coding the fourth dimension, 3D photos, etc. Amon