We'll talk about Homology Groups, the notions of chains, boundaries, and provide concrete examples of their computation. We'll explain Poincaré duality and introduce de Rham cohomology, which connects

Mr. Tengse was invited to visit the Infinite Pig Farm. The staff member is responsible for introducing him to the management model here. Staff member: Welcome to the Infinite Pig Farm. This is an infi

The previous 4D engine was based on WebGL. Now I have decided to try using the new WebGPU API to re-implement the 4D rendering engine. Thus, the new project - Tesserxel was born. Tesserxel takes the w

How do you play piano using a computer keyboard? Actually, there are many computer piano simulation softwares available, such as EveryOnePiano which I’ve used before, and the more famous FreePiano. Of

In previous article, we introduced various figures with holes in 4D. How to study these holes? This article aims to provide an intuition of homotopy and homology in algebraic topology.

The introduction to 2D surface knots wasn't actually very detailed last time. Today we want to analyze knots from another perspective. Let's try to unknot some knots in 4D space!

Here we introduce a new algebraic system that can "unify" high-dimensional geometry - Geometric Algebra. This encompasses scalars, vectors, n-vectors. It even includes spinors (rotate twice to look th

In our 3D world, one of the most magical things is the electromagnetic field. Various induction phenomena are 3D and require the right-hand rule in space. Can we analogize these things to 4D?