Associative magic square
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An associative magic square is a magic square for which each pair of numbers symmetrically opposite to the center sum up to the same value. For an n × n square, filled with the numbers from 1 to n2, this common sum must equal n2 + 1. These squares are also called associated magic squares, regular magic squares, regmagic squares, or symmetric magic squares.[1][2][3]
For instance, the Lo Shu Square – the unique 3 × 3 magic square – is associative, because each pair of opposite points form a line of the square together with the center point, so the sum of the two opposite points equals the sum of a line minus the value of the center point regardless of which two opposite points are chosen.[4] The 4 × 4 magic square from Albrecht Dürer's 1514 engraving Melencolia I – also found in a 1765 letter of Benjamin Franklin – is also associative, with each pair of opposite numbers summing to 17.[5]
