Rubik's Cube in the context of "Abstract algebra"

Trillion is a number with two distinct definitions:

• 1,000,000,000,000, i.e. one million million, or 10 (ten to the twelfth power), as defined on the short scale. This is now the meaning in both American and British English.
• 1,000,000,000,000,000,000, i.e. 10 (ten to the eighteenth power), as defined on the long scale. This is one million times larger than the short scale trillion. This is the historical meaning in English and the current use in many non-English-speaking countries where trillion and billion 10 (ten to the twelfth power) maintain their long scale definitions.

A combination puzzle, also known as a sequential move puzzle, is a puzzle which consists of a set of pieces which can be manipulated into different combinations by a group of operations. Many such puzzles are mechanical puzzles of polyhedral shape, consisting of multiple layers of pieces along each axis which can rotate independently of each other. Collectively known as twisty puzzles, the archetype of this kind of puzzle is the Rubik's Cube. Each rotating side is usually marked with different colours, intended to be scrambled, then solved by a sequence of moves that sort the facets by colour. Generally, combination puzzles also include mathematically defined examples that have not been, or are impossible to, physically construct.

Ernő Rubik (Hungarian: [ˈrubik ˈɛrnøː]; born 13 July 1944) is a Hungarian architect and inventor, widely known for creating the Rubik's Cube (1974), Rubik's Magic, and Rubik's Snake.

While Rubik became famous for inventing the Rubik's Cube and his other puzzles, much of his recent work involves the promotion of science in education. Rubik is involved with several organizations such as Beyond Rubik's Cube, the Rubik Learning Initiative and the Judit Polgar Foundation, all of which aim to engage students in science, mathematics, and problem solving at a young age.

Pentangle, later Pentangle Puzzles, was a British manufacturer and distributor of burr puzzles and other mechanical puzzles. It operated in the UK from 1971 until 2018. It was best known as the first company to distribute what became called "Rubik's Cube" outside Hungary.

Ideal Toy Company was an American toy company founded by Morris Michtom and his wife, Rose. During the post–World War II baby boom era, Ideal became the largest doll-making company in the United States. Their most popular dolls included Betsy Wetsy, Toni, Saucy Walker, Shirley Temple, Miss Revlon, Patti Playpal, Tammy, Thumbelina, Tiny Thumbelina, and Crissy. The company is also known for selling the Rubik's Cube.

Thomas Kremer (26 May 1930 – 24 June 2017) was a game inventor and marketer who acquired the rights to market the Rubik's Cube.

Tom Kremer was a games designer, entrepreneur and publisher, best known for his discovery and popularisation of the Rubik's Cube. As an octogenarian he founded the publishing house Notting Hill Editions, with the aim of reinvigorating the lost art of the essay.

In mathematics, a group is a set with an operation that combines any two elements of the set to produce a third element within the same set and the following conditions must hold: the operation is associative, it has an identity element, and every element of the set has an inverse element. For example, the integers with the addition operation form a group.

The concept of a group was elaborated for handling, in a unified way, many mathematical structures such as numbers, geometric shapes and polynomial roots. Because the concept of groups is ubiquitous in numerous areas both within and outside mathematics, some authors consider it as a central organizing principle of contemporary mathematics.

In abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right.

Various physical systems, such as crystals and the hydrogen atom, and three of the four known fundamental forces in the universe, may be modelled by symmetry groups. Thus group theory and the closely related representation theory have many important applications in physics, chemistry, and materials science. Group theory is also central to public key cryptography.