Magic Square


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magic square,

a square divided into parts with letters or numbers inscribed therein that, whether combined vertically, horizontally, or diagonally, form the same sum or the same word. In ancient times such squares were thought to have magic properties, perhaps connected with the stars. Magic squares have been found in such widely divergent cultures as ancient China, Egypt, and India, as well as W Europe. Example:

Bibliography

See W. S. Andrews, Magic Squares and Cubes (2d ed. 1917, repr. 1960).


square, magic:

see magic squaremagic square,
a square divided into parts with letters or numbers inscribed therein that, whether combined vertically, horizontally, or diagonally, form the same sum or the same word.
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Magic Square

 

a square divided into an equal number n of columns and rows with the resulting cells containing the first n2 natural numbers whose sum in each column, each row, and the two main diagonals is the same [being equal, as can be shown, to (½) n(n2 + 1)]. It has been proved that a magic square can be constructed for any n beginning with n = 3. Figure 1, a shows magic squares for n = 3 and n = 4. There exist magic squares that satisfy a number of additional conditions, as for example, a magic square with 64 cells (see Figure 1, b), which can be divided into four smaller squares each containing 16 cells such that the sum of the numbers of any row, any column, or the main diagonals is the same (130). Magic squares were used as talismans in India and some other countries. The construction of magic squares is a classical example of mathematical games and puzzles.

Figure 1

REFERENCE

Postnikov, M. M. Magicheskie kvadraty. Moscow, 1964.

magic square

[′maj·ik ′skwer]
(mathematics)
A square array of integers where the sum of the entries of each row, each column, and each diagonal is the same.
A square array of integers where the sum of the entries in each row and each column (but not necessarily each diagonal) is the same. Also known as semimagic square.
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We don't think any economist today would propose that you can hold all of the magic square variables constant at the same time, when each is affected by millions of independent decisions and several of the variables are pushing against each other.
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Number of Backtracks solving N-Queens (NQ) and Magic Square (MS) with different strategies Strategy NQ n=8 NQ n=16 NQ n=20 MS n=3 MS n=4 F + ID 10 542 10026 0 12 F + IDM 11 542 10026 1 51 MRV + ID 10 3 11 0 3 MRV + IDM 10 3 11 1 97 AMRV + ID 11 517 2539 4 1191 AMRV + IDM 11 517 2539 0 42 O + ID 10 542 10026 0 10 O + IDM 10 542 10026 1 29 Dynamic 6 404 629 1 23
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Page's synecdoche for the poetic imagination, which she variously compares to "the Bodleian," "a magic square," and "the number nine.
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Helio Oiticica's Invencao da cor, Penetravel Magic Square #5, De Luxe (Invention of Color, Penetrable Magic Square #5, De Luxe), 1977, another outsize sculpture in ebullient dialogue with its environment, was reconstructed at Inhotim following the detailed plans and sketches left by the late artist.
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