In my previous articles on 4D space, I described a world on a 4D planet. This time, I'll investigate the day-night and seasonal changes produced by a 4D planet's rotation and revolution. The first thi

To experience the "feeling" of 4D space, interactions on computer is really helpful. Here I'll organize the 4D programs I've played (not necessarily all games, 4DGolf、4DMiner、4D Toys、Miegakure、4DBlock

With some basic knowledge of groups, we should now discuss the problem of roots of n-degree equations. This article is somewhat advanced, but it aims to give readers an intuitive understanding of Galo

Why do quintic equations have no radical solutions? Galois provided a perfect answer using group theory. Most engineering students haven't studied group theory or abstract algebra. I plan to write a s

The Pythagorean theorem can be invalid! You've probably heard of non-Euclidean geometry. If we "forcibly" define the distance such that the sum of the p-th powers of the two sides equals the p-th powe

"Dimensions" film talks about using stereographic projection to create maps. But the world maps we are familiar with are not made this way. World maps use another type of projection, and the map it pr

We know that a cube can be obliquely sectioned to produce a regular hexagonal cross-section, which intersects 6 faces of the cube. Generalizing to 4D, a certain cross-cell intersects all 8 cells of a

I mentioned a circular disk pattern that appeared in the film "Dimensions：A walk through mathematics". Actually this pattern is as fascinating as 4D space - Hperbolic tessellation in hyperbolic space.