Rubik's Cube Each method of solving the Rubik's Cube employs its own set of algorithms, together with descriptions of what effect the algorithm has, and when it can be used to bring the cube closer to being solved. Many algorithms are designed to transform only a small part of the cube without interfering with other parts that have already been solved so that they can be applied repeatedly to different parts of the cube until the whole is solved. For example, there are well-known algorithms for cycling three corners without changing the rest of the puzzle or flipping the orientation of a
Principal root of unity Principal root of unity In mathematics, a principal "n"-th root of unity (where "n" is a positive integer) of a ring is an element formula_1 satisfying the equations In an integral domain, every primitive "n"-th root of unity is also a principal formula_3-th root of unity. In any ring, if formula_3 is a power of formula_5, then any formula_6-th root of formula_7 is a principal formula_3-th root of unity. A non-example is formula_9 in the ring of integers modulo formula_10; while formula_11 and thus formula_9 is a cube root of unity, formula_13 meaning that it is not a "principal" cube