The Secret Math Behind Solving a Rubik's Cube Like a Pro! скачать в хорошем качестве

The Secret Math Behind Solving a Rubik's Cube Like a Pro!

Summary: Dive deep into the fascinating world of Rubik's Cube solving with the power of stabilizer chains! In this video, we unravel the algorithmic secrets that make computers solve the Rubik's Cube effortlessly. Learn how configurations are mapped, orbits are analyzed, and transformations are executed to crack the 43 quintillion possibilities. Whether you're a cube enthusiast or curious about the math and programming behind the process, this video has something for you! The colorful Rubik's Cube is used as an excuse to talk about group theoretical notions such as permutations stabilizer (chains) orbits cosets As a side product we obtain a confirmation for the order of the Rubik's cube group that was estimated heuristically in our last video. This time, the order is the product of all orbit lengths contained in the stabilizer chain. Content: 0:00 Layer-by-Layer solution of the Rubik's Cube 3:15 Singmaster Notation 4:15 Bot solution 5:25 Overview - Table of Content 6:50 Symmetries of a Cube 9:01 Generating Set - Coxeter Group B3 11:00 The Group Tree 13:09 Simplifications of Words 14:42 Composition of Permutations 17:01 Orbits and Stabilizers 19:09 The First Orbit of the Rubik's Cube 20:24 Introduction to Stabilizer Chains 22:45 The Stabilizer Chain of the Rubik's Cube 25:00 The Order of the Rubik's Cube 25:28 Solve The Rubik's Cube with the Stabilizer Chain 29:15 Outlook Correction: 23:40 It's clear to see that four faces have been stabilized before. Therefore, the orbit length is 24-8=16. Sorry for this completely messed up sentence. It survived from an older version of the script, where a different stabilizer chain was used. References: Hulpke, A. (2010) Notes on Computational Group Theory. Department of Mathematics. Colorado State University.