A square matrix, usually divided into cells filled with numbers or letters in a significant arrangement. These squares were originally used for religious purposes, but in later times were employed as magic talismans or charms. The so-called “Sator” square is frequently met with in the West and it is of undoubted antiquity dating to at least 100 CE. The meaningless phrase conceals a cross:

S A T O R
A R E P O
T E N E T
O P E R A
R O T A S

In arithmetical squares the numbers are usually placed into cells and chosen so that every row, column and diagonal when added produce the same sum

4  9  2
3  5  7
8  1  6

Of late the mathematical structures possible in magic squares have interested many mathematicians as a statistical device which has been used in agronomy, medicine, psychology and other disciplines.

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