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Supercube

In: Applications of Fibonacci Numbers

Author

Listed:
  • Joseph Arkin
  • David C. Arney
  • Lee S. Dewald
  • Frank R. Giordano

Abstract

(1) In 1888, the first perfect magic cube ever constructed was of order 8, and was placed in “The Memoirs of the National Academy of Science” [3]. (2) Martin Gardner defines a perfect magic cube as follows: “A perfect magic cube is a cubical array of positive integers from 1 to N3 such that every straight line of N cells adds up to a constant. These lines include the orthogonals (the lines parallel to an edge), the two main diagonals of every orthogonal cross section and the four space diagonals. The constant is $$ (1 + 2 + 3 +... + {N^3})/{N^2} = \frac{1}{2}({N^4} + N)"[4]. $$ (3) E. G. Straus, in 1976, in a private letter to Arkin, described how he constructed a 7x7x7 perfect magic cube. This may be the lowest possible order of a perfect Latin 3-cube [5]. (4) In 1985, Arkin superimposed 6 orthogonal Latin cubes of order 7 to form 20 separate Latin 3-cubes [1]. (5) A perfect 4-dimensional hypercube of order 7 was constructed at West Point in 1989 [2].

Suggested Citation

  • Joseph Arkin & David C. Arney & Lee S. Dewald & Frank R. Giordano, 1991. "Supercube," Springer Books, in: G. E. Bergum & A. N. Philippou & A. F. Horadam (ed.), Applications of Fibonacci Numbers, pages 17-32, Springer.
    • Handle: RePEc:spr:sprchp:978-94-011-3586-3_3
    DOI: 10.1007/978-94-011-3586-3_3
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