Generalized Method for Constructing Magic Cube by Folded Magic Squares

Автор: Omar A. Dawood, Abdul Monem S. Rahma, Abdul Mohsen J. Abdul Hossen

Журнал: International Journal of Intelligent Systems and Applications(IJISA) @ijisa

Статья в выпуске: 1 vol.8, 2016 года.

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In the present paper we have developed a new method for constructing magic cube by using the folded magic square technique. The proposed method considers a new step towards the magic cube construction that applied a good insight and provides an easy generalized technique. This method generalized the design of magic cube with N order regardless the type of magic square whether odd order, singly even order or doubly even order. The proposed method is fairly easy, since it have depended mainly on the magic square construction methods, and all what the designer need is just how to builds six magic square sequentially or with constant difference value between each pair of the numbers in the square matrix, whereby each one of this magic square will represents the surface or dimension for magic cube configuration. The next step for the designer will be how to arrange each square in the proper order to constitute the regular cube in order to maintain the properties of magic cube, where the sum of rows, columns and the diagonals from all directions are the same.

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Magic Square, Magic Cube, Magic Constant, Magic Sum, Folded Square

Короткий адрес: https://sciup.org/15010781

IDR: 15010781

Список литературы Generalized Method for Constructing Magic Cube by Folded Magic Squares

  • Evel´ın Fonseca Cruz and Enguerran Grandchamp, “Heuristic Method to Find Magic Squares”, IEEE Computer Society, 15th International Conference on Computational Science and Engineering 2012.
  • Pickover, C. A.: The Zen of Magic Square, Circles and Stars: An Exhibition of Surprising Structures Across Dimensions, NJ: Princeton University Press, 2002.
  • B L Kaul, “Generalization of Magic Square (Numerical Logic) 3×3 and its Multiples (3×3) × (3×3)”, I.J. Intelligent Systems and Applications, 2013, 01, 90-97
  • H. D. Heinz & J. R. Hendricks, “MAGIC SQUARE LEXICON: ILLUSTRATED”, Copyright ? 2000 by Harvey D. Heinz.
  • B L Kaul and Ramveer Singh Generalization of Magic Square (Numerical Logic) 3×3 and its Multiples (3×3) × (3×3), I.J. Intelligent Systems and Applications, 2013, 01, 90-97.
  • Tomba I and Shibiraj N, “Improved Technique for Constructing Doubly-even Magic Squares using Basic Latin Squares”, International Journal of Scientific and Research Publications, Volume 3, Issue 6, June 2013.
  • John Hendricks, “The Diagonal Rule for Magic Cubes of Odd Order,” Journal of Recreational Mathematics 20(4):192—195 (1988).
  • William H. Benson and Oswald Jacoby, “MAGIC CUBES New Recreations”, Dover Publications, Inc., in 1981.
  • C.A. Pickover, The Zen of magic squares, circles, and stars, Princeton University Press, Princeton, NJ, 2002.
  • D.I. George, J.Sai Geetha and K.Mani, “Add-on Security Level for Public Key Cryptosystem using Magic Rectangle with Column/Row Shifting”, International Journal of Computer Applications (0975 – 8887) Volume 96– No.14, pp. 38-43, June 2014.
  • Nitin Pandey, D.B.Ojha, “SECURE COMMUNICATION SCHEME WITH MAGIC SQUARE”, Volume 3, No. 12, pp. 12-14 December 2012.
  • Gopinanath Ganapathy, and K. Mani, “Add-On Security Model for Public-Key Cryptosystem Based on Magic Square Implementation”, Proceedings of the World Congress on Engineering and Computer Science, San Francisco, USA, Vol I, 2009.
  • Ronald P. Nordgren, “NEW CONSTRUCTIONS FOR SPECIAL MAGIC SQUARES”, International Journal of Pure and Applied Mathematics, Volume 78 No. 2, pp 133-154, Academic Publications, Ltd.2012.
  • Adam Rogers, and Peter Loly, “The Inertial Properties of Magic Squares and Cubes”, Nov. 2004, pp. 1-3.
  • Tao Xie and Lishan Kang, “An Evolutionary Algorithm for Magic Squares”, IEEE, 2003.
  • FRANK J. SWETZ, “Legacy of the Luoshu”, The 4,000 Year Search for the Meaning of the Magic Square of Order Three, A K Peters, Ltd. Wellesley, Massachusetts, 2008.
  • Andrews, W. S. Magic Squares and Cubes. Chicago: SECOND EDITION. REVISED AND ENLARGED Open Court Publishing, 1917.
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