Perfect magic cube

In mathematics, a perfect magic cube is a magic cube in which not only the columns, rows, pillars, and main space diagonals, but also the cross section diagonals sum up to the cube's magic constant.[1][2][3]

Perfect magic cubes of order one are trivial; cubes of orders two to four can be proven not to exist,[4] and cubes of orders five and six were first discovered by Walter Trump and Christian Boyer on November 13 and September 1, 2003, respectively.[5] A perfect magic cube of order seven was given by A. H. Frost in 1866, and on March 11, 1875, an article was published in the Cincinnati Commercial newspaper on the discovery of a perfect magic cube of order 8 by Gustavus Frankenstein. Perfect magic cubes of orders nine and eleven have also been constructed. The first perfect cube of order 10 was constructed in 1988 (Li Wen, China).[6]

  1. ^ W., Weisstein, Eric. "Perfect Magic Cube". mathworld.wolfram.com. Retrieved 4 December 2016.{{cite web}}: CS1 maint: multiple names: authors list (link)
  2. ^ Alspach, Brian; Heinrich, Katherine. "Perfect Magic Cubes of Order 4m" (PDF). Retrieved 3 December 2016.
  3. ^ Weisstein, Eric W. (12 December 2002). CRC Concise Encyclopedia of Mathematics, Second Edition. CRC Press. ISBN 9781420035223.
  4. ^ Pickover, Clifford A. (28 November 2011). The Zen of Magic Squares, Circles, and Stars: An Exhibition of Surprising Structures across Dimensions. Princeton University Press. ISBN 978-1400841516.
  5. ^ "Perfect Magic Cubes". www.trump.de. Retrieved 4 December 2016.
  6. ^ Cite error: The named reference :1 was invoked but never defined (see the help page).