Group theory 101: How to play a Rubik’s Cube like a piano - Michael Staff
View full lesson: http://ed.ted.com/lessons/group-theory-101-how-to-play-a-rubik-s-cube-like-a-piano-michael-staff Mathematics explains the workings of the ...
==========
How can you play a Rubik's Cube? Not play with it, but play it like a piano? That question doesn't make a lot of sense at first, but an abstract mathematical field called group theory holds the answer, if you'll bear with me. In math, a group is a particular collection of elements. That might be a set of integers, the face of a Rubik's Cube, or anything, so long as they follow four specific rules, or axioms. Axiom one: all group operations must be closed or restricted to only group elements. So in our square, for any operation you do, like turn it one way or the other, you'll still wind up with an element of the group. Axiom two: no matter where we put parentheses when we're doing a single group operation, we still get the same result. In other words, ...
==========
How can you play a Rubik's Cube? Not play with it, but play it like a piano? That question doesn't make a lot of sense at first, but an abstract mathematical field called group theory holds the answer, if you'll bear with me. In math, a group is a particular collection of elements. That might be a set of integers, the face of a Rubik's Cube, or anything, so long as they follow four specific rules, or axioms. Axiom one: all group operations must be closed or restricted to only group elements. So in our square, for any operation you do, like turn it one way or the other, you'll still wind up with an element of the group. Axiom two: no matter where we put parentheses when we're doing a single group operation, we still get the same result. In other words, ...
