Bimagic cube

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 David M. Collison apparently constructed a bimagic cube of order 25 in an unpublished paper, but it was not until the year 2000 that John Hendricks published an order 25 perfect magic cube whose square is a semiperfect magic cube. It has order 25 and magic constant 195325

On January 20, 2003, Christian Boyer discovered an order 16 bimagic cube (where the cube itself is perfect magic, but its square is only semiperfect magic). This was rapidly followed by another order 16 bimagic cube (where the base cube is perfect and its square semiperfect) on January 23, an order 32 bimagic cube (where both the base cube and its square are perfect) on January 27, and an order 27 bimagic cube (where the base cube is perfect but its square is semiperfect) on February 3, 2003.

Boyer's 16-cubes thus became the smallest known bimagic cube, and his order 32 cube became the first known perfect bimagic cube.

See also

* Magic cube
* Trimagic cube
* Multimagic cube
* Magic square
* Bimagic square
* Trimagic square
* Multimagic square


Wikimedia Foundation. 2010.

Игры ⚽ Нужно решить контрольную?

Look at other dictionaries:

  • 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

  • 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 …   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

  • 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

  • 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

  • John R. Hendricks — John Robert Hendricks (September 4 1929 July 7 2007) was a mathematician specializing in magic squares and hypercubes. He has published many articles in the Journal of Recreational Mathematics as well as other Journals. Early yearsJohn Robert… …   Wikipedia

  • List of mathematics articles (B) — NOTOC B B spline B* algebra B* search algorithm B,C,K,W system BA model Ba space Babuška Lax Milgram theorem Baby Monster group Baby step giant step Babylonian mathematics Babylonian numerals Bach tensor Bach s algorithm Bachmann–Howard ordinal… …   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

  • 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 square — In recreational mathematics, a magic square of order n is an arrangement of n2 numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant.[1] A normal magic… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”