Rubik S Cube Mathematical Model

If x and y are two moves on rubik s cube theircommutatoris the move xyx1y1.

Rubik s cube mathematical model. A mathematical approach to solving rubik s cube by raymond tran ubc math308 fall 2005 history. When yx xy thus the commutator of x and y measures the failure of x and y to commute. There is an identity element e g such that e g g e g. In 1974 rubik patented his creation in hungary and in 1977 sales in the country began.

Every element in g has an inverse g 1relative to the operation such that g g 1 g 1 g e. Just a couple of years later toy company ideal negotiated an agreement to sell the cube worldwide. Solving the rubik s cube has nothing to do with magic but everything to do with maths. Xyx1y1 1 exactly when x and y commute.

The main objective when using one is to recreate it s original position a solid color for each. The rubik s cube is an instance of what s called a configuration problem the best known example of which involves finding the most efficient way to reorganize boxes stacked in a warehouse. Because xyx1y1 xy yx 1 which equals the identity when yx 1is the inverse of xy i e. We turn the cube and it twists us erno rubik the rubiks cube is a cube consisting of 6 sides with 9 individual pieces on each.