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Bimagic Square

\begin{figure}\begin{center}\BoxedEPSF{BimagicSquare.epsf scaled 1000}\end{center}\end{figure}

If replacing each number by its square in a Magic Square produces another Magic Square, the square is said to be a bimagic square. The first bimagic square (shown above) has order 8 with magic constant 260 for addition and 11,180 after squaring. Bimagic squares are also called Doubly Magic Squares, and are 2-Multimagic Squares.

See also Magic Square, Multimagic Square, Trimagic Square


Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed. New York: Dover, p. 212, 1987.

Hunter, J. A. H. and Madachy, J. S. ``Mystic Arrays.'' Ch. 3 in Mathematical Diversions. New York: Dover, p. 31, 1975.

Kraitchik, M. ``Multimagic Squares.'' §7.10 in Mathematical Recreations. New York: W. W. Norton, pp. 176-178, 1942.

© 1996-9 Eric W. Weisstein