词条 | Multimagic cube |
释义 |
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]References1. ^{{MathWorld|id=MultimagicCube}} 2. ^{{MathWorld|title=Bimagic Cube|id=BimagicCube}} 3. ^{{MathWorld|id=TriMagic|title=Trimagic Cube}} 4. ^{{MathWorld|title=Tetramagic Cube|id=TetramagicCube}} See also
1 : Magic squares |
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