Magic Square - Wikipedia, the Free Encyclopedia
Magic square - Wikipedia, the free encyclopedia http://en.wikipedia.org/wiki/Magic_square You can support Wikipedia by making a tax-deductible donation. Magic square From Wikipedia, the free encyclopedia In recreational mathematics, a magic square of order n is an arrangement of n² numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant.[1] A normal magic square contains the integers from 1 to n². The term "magic square" is also sometimes used to refer to any of various types of word square. Normal magic squares exist for all orders n ≥ 1 except n = 2, although the case n = 1 is trivial—it consists of a single cell containing the number 1. The smallest nontrivial case, shown below, is of order 3. The constant sum in every row, column and diagonal is called the magic constant or magic sum, M. The magic constant of a normal magic square depends only on n and has the value For normal magic squares of order n = 3, 4, 5, …, the magic constants are: 15, 34, 65, 111, 175, 260, … (sequence A006003 in OEIS). Contents 1 History of magic squares 1.1 The Lo Shu square (3×3 magic square) 1.2 Cultural significance of magic squares 1.3 Arabia 1.4 India 1.5 Europe 1.6 Albrecht Dürer's magic square 1.7 The Sagrada Família magic square 2 Types of magic squares and their construction 2.1 A method for constructing a magic square of odd order 2.2 A method of constructing a magic square of doubly even order 2.3 The medjig-method of constructing magic squares of even number
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