Multimagic cube
≈ 2 min read
Names in other languages
- FrançaisCube multimagique
- ItalianoCubo multimagico
- EnglishMultimagic cube
- 中文多魔术正方体
- 中文多魔术正方体
- 简体中文多魔术正方体
- 繁體中文多魔術正方體
Article bodies are English and are not machine-translated. A name in another language is not a translation of the article.
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.
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.
Text derived from https://en.wikipedia.org/w/index.php?oldid=1327686157 under CC BY-SA 4.0; modifications have been made.