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  2. Doubling the cube - Wikipedia

    en.wikipedia.org/wiki/Doubling_the_cube

    In algebraic terms, doubling a unit cube requires the construction of a line segment of length x, where x 3 = 2; in other words, x = , the cube root of two. This is because a cube of side length 1 has a volume of 1 3 = 1 , and a cube of twice that volume (a volume of 2) has a side length of the cube root of 2.

  3. Sphere packing in a cylinder - Wikipedia

    en.wikipedia.org/wiki/Sphere_packing_in_a_cylinder

    Illustration of a columnar structure assembled by golf balls. Sphere packing in a cylinder is a three-dimensional packing problem with the objective of packing a given number of identical spheres inside a cylinder of specified diameter and length.

  4. Descent into the Depths of the Earth - Wikipedia

    en.wikipedia.org/wiki/Descent_into_the_Depths_of...

    g1 g2 g3 d1 d2 d3 q1 Descent Into the Depths of the Earth [ 2 ] is an adventure module for the Dungeons & Dragons ( D&D ) fantasy roleplaying game coded D1–2. It was written by Gary Gygax , and combines two previously published modules from 1978, the original Descent into the Depths of the Earth and Shrine of the Kuo-Toa .

  5. Hoffman's packing puzzle - Wikipedia

    en.wikipedia.org/wiki/Hoffman's_packing_puzzle

    Each valid solution to the puzzle arranges the blocks in an approximate 3 × 3 × 3 grid of blocks, with the sides of the blocks all parallel to the sides of the outer cube, and with one block of each width along each axis-parallel line of three blocks. Counting reflections and rotations as being the same solution as each other, the puzzle has ...

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

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

    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. Given a random cube C, it is solved as iterative deepening. First all ...

  7. Cubic metre per second - Wikipedia

    en.wikipedia.org/wiki/Cubic_metre_per_second

    Cubic metre per second or cubic meter per second in American English (symbol m 3 ⋅ s −1 or m 3 /s) is the unit of volumetric flow rate in the International System of Units (SI). It corresponds to the exchange or movement of the volume of a cube with sides of one metre (39.37 in) in length (a cubic meter , originally a stere ) each second .

  8. Cubical complex - Wikipedia

    en.wikipedia.org/wiki/Cubical_complex

    Equivalently, an elementary cube is any translate of a unit cube [,] embedded in Euclidean space (for some , {} with ). [3] A set X ⊆ R d {\displaystyle X\subseteq \mathbf {R} ^{d}} is a cubical complex (or cubical set ) if it can be written as a union of elementary cubes (or possibly, is homeomorphic to such a set).

  9. Dihedral group of order 6 - Wikipedia

    en.wikipedia.org/wiki/Dihedral_group_of_order_6

    Consider three colored blocks (red, green, and blue), initially placed in the order RGB. The symmetric group S 3 is then the group of all possible rearrangements of these blocks. If we denote by a the action "swap the first two blocks", and by b the action "swap the last two blocks", we can write all possible permutations in terms of these two ...