Answer:
Magic square is a square divided into smaller squares each containing a number, such that the figures in each vertical, horizontal, and diagonal row add up to the same value.
How does it work ?
A magic square is an n x n square with a whole number written inside each cell, so that the sum of the numbers in every row, in every column and in each of the main diagonals is equal. This number is called the magic number. The main diagonals are those that stretch from corner to corner.
Why magic square is called as magic square ?
The magic square gets its name because all the rows, columns, and diagonals add up to the same sum, which is called the magic constant.
Who created Magic square ?
In the 18th century, Leonhard Euler, the greatest mathematician of his day, was devising ways to create magic squares. In order to do this he started looking at another type of square that could be used as a kind of template for producing magic squares.
Explanation:
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.
M2(n)=1/n sum_(k=1)^(n^2)k=1/2n(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.
The unique normal square of order three was known to the ancient Chinese, who called it the Lo Shu. A version of the order-4 magic square with the numbers 15 and 14 in adjacent middle columns in the bottom row is called Dürer's magic square. Magic squares of order 3 through 8 are shown above.
[ Refer : https://mathworld.wolfram.com/MagicSquare.html }
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