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Magic Square

Alternate names

diagonally magic square | normal magic square

Basic definition

A magic square is a square array of positive integers such that the sum of any row, column, or main diagonal equals that of any other.

Detailed definition

A magic square is a square array of numbers consisting of the distinct positive integers 1, 2, ..., n^2 arranged such that the sum of the n numbers in any horizontal, vertical, or main diagonal line is always the same number, known as the magic constant M_2(n) = 1/n sum_(k = 1)^(n^2) k = 1/2 n(n^2 + 1). If every number in a magic square is subtracted from n^2 + 1, another magic square is obtained called the complementary magic square. A square consisting of consecutive numbers starting with 1 is sometimes known as a "normal" magic square.

Related terms

addition-multiplication magic square | alphamagic square | antimagic square | associative magic square | bimagic square | border square | Dürer's magic square | Euler square | Franklin magic square | gnomon magic square | heterosquare | Latin square | magic circles | magic constant | magic cube | magic hexagon | magic labeling | magic series | magic tesseract | magic tour | multimagic square | multiplication magic square | panmagic square | semimagic square | talisman square | templar magic square | trimagic square

Educational grade level

college level

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