![]() Is purported to have been first reported in the West when de la Loubere returned The method, also called de la Loubere's method, That is already filled, the next number is instead placed below the previous On the bottom and falling off the right returns on the left. The counting is wrapped around, so that falling off the top returns Row, then incrementally placing subsequent numbers in the square one unit above and It begins by placing a 1 in the center square of the top Technique known as the Siamese method can be used, as illustrated above (Kraitchikġ942, pp. 148-149). Kraitchik (1942) gives general techniques of constructing even and odd squares of order. In addition, squares that are magic under both addition and multiplicationĬan be constructed and are known as addition-multiplication Squares that are magic under multiplication instead of addition can be constructed and are known as multiplication magic squares. The square is said to be an associative magic If all pairs of numbers symmetrically opposite Produces another magic square, the square is said to be a bimagic Square (also called a diabolic square or pandiagonal square). Those obtained by wrapping around) of a magic square sum to the magicĬonstant, the square is said to be a panmagic (1982) and onĪ square that fails to be magic only because one or both of the main diagonal sums do not equal the magic constant is called a semimagic square. ![]() Methods forĮnumerating magic squares are discussed by Berlekamp et al. Using Monte Carlo simulation and methods from statistical mechanics. The number of squares is not known, but Pinn and Wieczerkowski (1998) Magic squares was computed by R. Schroeppel in 1973. The 880 squares of order four were enumerated by Frénicleĭe Bessy in 1693, and are illustrated in Berlekamp et al. Otherwise, numbered squares have always been far more significant, particularly in China (where they may have originated), the Arab world, and India.It is an unsolved problem to determine the number of magic squares of an arbitrary order, but the number of distinct magic squares (excluding those obtained by rotationĢ. Examples of this square from the 1st century ad were found in the ruins of Pompeii, and it was still employed during the 19th century in Europe and the United States for fancied protection against fire, sickness, and other disasters. Arranged both vertically and horizontally, the meaningless phrase reads through the centre TENET, thus forming the two arms of a hidden cross. The most familiar lettered square in the Western world is the well-known SATOR square, composed of the words SATOR, AREPO, TENET, OPERA, and ROTAS. Originally used as religious symbols, they later became protective charms or tools for divination and finally, when the original meanings were lost, people considered them mere curiosities or puzzles-except for some Western mathematicians who continue to study them as problems in number theory. Magic square, square matrix often divided into cells, filled with numbers or letters in particular arrangements that were once thought to have special, magical properties.
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