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  2. Cube (algebra) - Wikipedia

    en.wikipedia.org/wiki/Cube_(algebra)

    The cube of a number n is denoted n 3, using a superscript 3, [a] for example 2 3 = 8. The cube operation can also be defined for any other mathematical expression, for example (x + 1) 3. The cube is also the number multiplied by its square: n 3 = n × n 2 = n × n × n. The cube function is the function x ↦ x 3 (often denoted y = x 3) that

  3. Squared triangular number - Wikipedia

    en.wikipedia.org/wiki/Squared_triangular_number

    Alternatively, one can decompose the table into a sequence of nested gnomons, each consisting of the products in which the larger of the two terms is some fixed value. The sum within each gmonon is a cube, so the sum of the whole table is a sum of cubes. [6] Visual demonstration that the square of a triangular number equals a sum of cubes.

  4. Sum of two cubes - Wikipedia

    en.wikipedia.org/wiki/Sum_of_two_cubes

    A Cabtaxi number is the smallest positive number that can be expressed as a sum of two integer cubes in n ways, allowing the cubes to be negative or zero as well as positive. The smallest cabtaxi number after Cabtaxi(1) = 0, is Cabtaxi(2) = 91, [ 5 ] expressed as:

  5. Optimal solutions for the Rubik's Cube - Wikipedia

    en.wikipedia.org/wiki/Optimal_solutions_for_the...

    The cube restricted to only the corners, not looking at the edges; The cube restricted to only 6 edges, not looking at the corners nor at the other edges. The cube restricted to the other 6 edges. Clearly the number of moves required to solve any of these subproblems is a lower bound for the number of moves needed to solve the entire cube.

  6. Cake number - Wikipedia

    en.wikipedia.org/wiki/Cake_number

    The cake number is so-called because one may imagine each partition of the cube by a plane as a slice made by a knife through a cube-shaped cake. It is the 3D analogue of the lazy caterer's sequence. The values of C n for n = 0, 1, 2, ... are given by 1, 2, 4, 8, 15, 26, 42, 64, 93, 130, 176, 232, ... (sequence A000125 in the OEIS).

  7. Rubik's Cube group - Wikipedia

    en.wikipedia.org/wiki/Rubik's_Cube_group

    The Rubik's Cube group (,) represents the structure of the Rubik's Cube mechanical puzzle. Each element of the set corresponds to a cube move, which is the effect of any sequence of rotations of the cube's faces. With this representation, not only can any cube move be represented, but any position of the cube as well, by detailing the cube ...

  8. Cuban prime - Wikipedia

    en.wikipedia.org/wiki/Cuban_prime

    The formula for a general cuban prime of this kind can be simplified to + +. This is exactly the general form of a centered hexagonal number ; that is, all of these cuban primes are centered hexagonal.

  9. Rubik's Revenge - Wikipedia

    en.wikipedia.org/wiki/Rubik's_Revenge

    A solved Rubik's Revenge cube. The Rubik's Revenge (also known as the 4×4×4 Rubik's Cube) is a 4×4×4 version of the Rubik's Cube.It was released in 1981. Invented by Péter Sebestény, the cube was nearly called the Sebestény Cube until a somewhat last-minute decision changed the puzzle's name to attract fans of the original Rubik's Cube. [1]

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