Rubik's Cube literally took the world by storm in the early 1980's,
winning England's "Toy of the Year" award for two consecutive years (1980
and 1981) and becoming one of the best-selling toys ever. The Cube
was so popular during the early part of the decade that the entire decade
is now
associated with the Cube and an entire generation of children grew
up with a Cube in their hands.
Ernö Rubik actually invented his Magic Cube in 1974. A teacher of three-dimensional design at the Academy of Applied Art in Budapest, Rubik designed his Cube to help teach his students to think in three dimensions and to develop spatial reasoning skills. He did not envision the immense popularity that his puzzle would obtain, nor could he imagine the impact that his Cube would have on the world of mathematics.
Besides being a fun toy and a useful tool for teaching three-dimensional reasoning, Rubik's Cube is also
a very elegant example of a permutation group . . . [with] so much complexity that one really must use mathematics to understand the cube's potential . . . The mathematical aspects [of the cube] range from simple investigations suitable for school students up to research problems leading to general unsolved problems in group theory (Singmaster x).Given the construction of the Cube, it has a great many possible permutations (4.3 x 10E19) and some intriguing physical properties. Of greater mathematical importance are its properties as a group that make it an object for group theorists to study, and some mathematicians have devoted significant time to constructing the most efficient algorithm to solve the Cube. Currently, an algorithm developed by the English mathematician Morwen B. Thistlewaite uses the fewest rotations, 50, to restore a cube to its solved position, but, theoretically, "God's Algorithm" is the most efficient algorithm possible and could solve the Cube in as few as 22 rotations.
Author: Tony Brinsko
References:
Frey, Alexander H., Jr. and David Singmaster. Handbook of
Cubic Math. Hillside, NJ: Enslow Publishers, 1982.
Singmaster, David. Notes on Rubik's Magic Cube. Hillside, NJ: Enslow Publishers, 1981.
—, ed. Rubik's Cubic Compendium. New York: Oxford University Press, 1987.
Kéri, Gerzson. "Restoration Methods and Tables of Processes." Singmaster, ed. 95-145.
Rubik, Ernö. "In Play." Singmaster, ed. 1-17.
Singmaster, David. Introduction. Singmaster, ed. vii-xi.
|
|
|
|
|
|