#211. HYPERCUBE and the fourth dimension

How exactly does the hypercube rotate in the famous GIF image? Are the faces of a four-dimensional cube (tesseract) squares (as many people think) or something else? How can 4D shapes be depicted? How is an n-dimensional cube structured? Everything will become clear in this episode! My courses: https://vk.com/market-135395111 VK: https://vk.com/wildmathing Problem book: https://vk.com/topic-135395111_35874038 Donate: http://www.donationalerts.ru/r/wildma... In this episode, we'll also understand the connection between the n-dimensional hypercube and Newton's binomial theorem. We'll understand how many six-dimensional faces a seven-dimensional cube has, and we'll also explore how faces of dimension n are structured, how many there are, and why. And, of course, to understand 4D geometry, we need to brush up on central projection and concurrent projection: let's do just that using the example of a 4D hypercube! 0:00 — Summary 0:15 — 1D Cube 0:50 — 2D Cube 2:25 — 3D Cube 4:27 — 4D Cube 7:42 — Parallel and Central Projection 9:47 — Hypercube Animation OTHER VIDEOS ABOUT INCREDIBLY INTERESTING MATH 1. The first episode about 4D Geometry:    • #210. ВОЗМОЖНОСТИ ЧЕТВЕРТОГО ИЗМЕРЕНИЯ   2. Why do we need mathematics:    • #200. ЗАЧЕМ НУЖНА МАТЕМАТИКА?   3. How to extract long roots:    • #140. КАК ИЗВЛЕКАТЬ КОРНИ В СТОЛБИК? В ШКО...   4. The most beautiful formula in mathematics:    • #161. САМАЯ КРАСИВАЯ ФОРМУЛА В МАТЕМАТИКЕ ...   5. The Riemann Hypothesis:    • #170. ГИПОТЕЗА РИМАНА — ПРОБЛЕМА ТЫСЯЧЕЛЕТИЯ!   #Science #Mathematics #Popular Science LITERATURE Galperin, G. A., The Multidimensional Cube: https://mccme.ru/free-books/mmmf-lect... Smirnova, I. M., Smirnov, V. A., Four-Dimensional Geometry Zorich, V. A., Mathematical Analysis