Multimagic cube

In mathematics, a P-multimagic cube is a magic cube that remains magic even if all its numbers are replaced by their k-th power for 1 ≤ k ≤ P. Thus, a magic cube is bimagic when it is 2-multimagic, and trimagic when it is 3-multimagic, tetramagic when it is 4-multimagic. ^[1] A P-multimagic cube is said to be semi-perfect if the k-th power cubes are perfect for 1 ≤ k < P, and the P-th power cube is semiperfect. If all P of the power cubes are perfect, the multimagic cube is said to be perfect.

The first known example of a bimagic cube was given by John Hendricks in 2000; it is a semiperfect cube of order 25 and magic constant 195325. In 2003, C. Bower discovered two semi-perfect bimagic cubes of order 16, and a perfect bimagic cube of order 32.^[2]

MathWorld reports that only two trimagic cubes are known, discovered by C. Bower in 2003; a semiperfect cube of order 64 and a perfect cube of order 256.^[3] It also reports that he discovered the only two known tetramagic cubes, a semiperfect cube of order 1024, and perfect cube of order 8192.^[4]

References

1. ^ Weisstein, Eric W., "Multimagic cube" from MathWorld.
2. ^ Weisstein, Eric W., "Bimagic Cube" from MathWorld.
3. ^ Weisstein, Eric W., "Trimagic Cube" from MathWorld.
4. ^ Weisstein, Eric W., "Tetramagic Cube" from MathWorld.

See also

• Magic square
• Multimagic square

This geometry-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Magic squares Geometry stubs Wikimedia Foundation. 2010. Игры ⚽ Поможем сделать НИР Tensor product of algebras Sravana Kumar Look at other dictionaries: Multimagic square — In mathematics, a P multimagic square (also known as a satanic square) is a magic square that remains magic even if all its numbers are replaced by their kth power for 1 ≤ k ≤ P. Thus, a magic square is bimagic if it is 2 multimagic, and trimagic …   Wikipedia Magic cube — For the flashbulb cartridges, see Magicube. For the puzzle, see Rubik s Cube. In mathematics, a magic cube is the 3 dimensional equivalent of a magic square, that is, a number of integers arranged in a n x n x n pattern such that the sum of the… …   Wikipedia Bimagic cube — In mathematics, a bimagic cube is a magic cube that also remains magic if all of the numbers it contains are squared. In 1934, Cazalas attempted but failed to construct a bimagic cube. David M. Collison apparently constructed a bimagic cube of… …   Wikipedia Trimagic cube — In mathematics, a trimagic cube is a magic cube that also remains magic if all of the numbers it contains are squared or cubed. Only two trimagic cubes are known. The first trimagic cube was found by C. Boyer on February 1, 2003 and is of order… …   Wikipedia Diagonal magic cube — A Diagonal Magic Cube is an improvement over the simple magic cube. It is the second of six magic cube classes when ranked by the number of lines summing correctly. In a diagonal magic cube of order m, all 6m of the diagonals in the m planes… …   Wikipedia Simple magic cube — A simple magic cube is the lowest of six basic classes of magic cube. These classes are based on extra features required.The simple magic cube requires only the basic features a cube requires to be magic. Namely; all lines parallel to the faces,… …   Wikipedia List of recreational number theory topics — This is a list of recreational number theory topics (see number theory, recreational mathematics). Listing here is not pejorative: many famous topics in number theory have origins in challenging problems posed purely for their own sake. See list… …   Wikipedia Bimagic square — In mathematics, a bimagic square is a magic square that also remains magic if all of the numbers it contains are squared. The first known bimagic square has order 8 and magic constant 260; it has been conjectured by Bensen and Jacoby that no… …   Wikipedia Trimagic square — In mathematics, a trimagic square is a magic square that also remains magic if all of the numbers it contains are squared or cubed. Trimagic squares of orders 12, 32, 64, 81 and 128 have been discovered so far; the only known trimagic square of… …   Wikipedia List of mathematics articles (M) — NOTOC M M estimator M group M matrix M separation M set M. C. Escher s legacy M. Riesz extension theorem M/M/1 model Maass wave form Mac Lane s planarity criterion Macaulay brackets Macbeath surface MacCormack method Macdonald polynomial Machin… …   Wikipedia 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”