magic square

magic squaretop: the SATOR letter squarebottom: the number square from Albrecht Dürer's engraving Melencolia I

magic square

n.1. A square that contains numbers arranged in equal rows and columns such that the sum of each row, column, and sometimes diagonal is the same.2. A similar square containing letters in particular arrangements that spell out the same word or words.

magic square

n (Mathematics) a square array of rows of integers arranged so that the sum of the integers is the same when taken vertically, horizontally, or diagonally

mag′ic square′

n. a square containing integers arranged in an equal number of rows and columns so that the sum of the integers in any row, column, or diagonal is the same. [1695–1705]

magic square

A square made up of smaller squares each containing a number, popular with magicians for making talismans.

Thesaurus

Noun

magic square - a square matrix of n rows and columns; the first n^2 integers are arranged in the cells of the matrix in such a way that the sum of any row or column or diagonal is the samesquare matrix - a matrix with the same number of rows and columns

Magic Square

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.

magic square

magic square

magic square

mag′ic square′

magic square

Magic Square

magic square,

Bibliography

square, magic:

Magic Square

REFERENCE

magic square

magic square

Words related to magic square

noun a square matrix of n rows and columns

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