Lesson plan
Multimagic cube
In mathematics, a P-multimagic cube is a magic cube that remains magic even if all its numbers are replaced by their kth powers for 1 ≤ k ≤ P. cubes are called bimagic, cubes are called trimagic, and cubes tetramagic. A cube is said to be semi-perfect if the kth power cubes are perfect for 1 ≤ k < P, and the Pth power cube is semiperfect. If all P of the power cubes are perfect, the 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. 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. It also reports that he discovered the only two known tetramagic cubes, a semiperfect cube of order 1024, and perfect cube of order 8192. In 2011, Emlyn Ellis Addison found a mod-9 symmetric semiperfect tetramagic cube of order 9, intended as a methodology for structuring musical compositions.
Article summary
In mathematics, a P-multimagic cube is a magic cube that remains magic even if all its numbers are replaced by their kth powers for 1 ≤ k ≤ P. cubes are called bimagic, cubes are called trimagic, and cubes tetramagic. A cube is said to be semi-perfect if the kth power cubes are perfect for 1 ≤ k < P, and the Pth power cube is semiperfect. If all P of the power cubes are perfect, the 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. 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. It also reports that he discovered the only two known tetramagic cubes, a semiperfect cube of order 1024, and perfect cube of order 8192. In 2011, Emlyn Ellis Addison found a mod-9 symmetric semiperfect tetramagic cube of order 9, intended as a methodology for structuring musical compositions.
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
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Key claims and bibliography are generated from the same tracked claims and sources as the article page.