TED-ED: Group theory 101: How to play a Rubik's Cube like a piano - Michael Staff

The video explores group theory, a mathematical field that explains how elements form groups by following four axioms: closure, associativity, identity, and inverses. It demonstrates the application of group theory in solving a Rubik's Cube by analyzing permutations and in music through chord inversions. The video highlights the versatility of group theory in different domains, showing its role in both puzzle solving and musical composition.

Which of the following is NOT one of the four axioms that define a mathematical group?

• Identity

• Commutativity

• Inverses

• Closure

How does group theory assist in solving a Rubik's Cube?

• By providing a random sequence of moves

• By analyzing permutations to find a solution

• By reducing the number of possible moves

• By changing the colors of the cube

In the context of group theory, what is a permutation?

• A mathematical equation

• A specific arrangement of elements

• A sequence of operations

• A type of musical chord

What is the term used in music for shifting the bottom note of a chord to the top?

• Rotation

• Permutation

• Transposition

• Inversion

How can a Rubik's Cube be related to music using group theory?

• By using musical notes to label the cube's faces

• By expressing the solution as a chord progression

• By assigning a note to each color

• By playing music while solving the cube