The third order magic square was known to Chinese mathematicians as early as 190 BCE, and explicitly given by the first century of the common era. Iron plate with an order 6 magic square in Eastern Arabic numerals from China, dating to the Yuan Dynasty (1271–1368).
There are also more specific strategies like the continuous enumeration method that reproduces specific patterns. Although completely general methods for producing all the magic squares of all orders do not exist, historically three general techniques have been discovered: by bordering method, by making composite magic squares, and by adding two preliminary squares. The mathematical study of magic squares typically deals with its construction, classification, and enumeration. When all the rows and columns but not both diagonals sum to the magic constant we have semimagic squares (sometimes called orthomagic squares). Some well-known examples, including the Sagrada Família magic square and the Parker square are trivial in this sense.
Magic squares that include repeated entries do not fall under this definition and are referred to as trivial. Some authors take magic square to mean normal magic square.
, n 2, the magic square is said to be normal.
If the array includes just the positive integers 1, 2. The order of the magic square is the number of integers along one side ( n), and the constant sum is called the magic constant. In recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same. The smallest (and unique up to rotation and reflection) non-trivial case of a magic square, order 3