Introduction and History :
A Magic Square with a side of value n is a matrix of size and is filled by the numbers from 1 to having the sum of all rows, columns and diagonals is the same.
The Magic Square is said to originate in China approximately at 650 B.C. There is an ancient myth in China that says while the Emperor Yu walked in front of the Yellow River, he saw a tortoise that had a pattern on its shell that looked like a 3x3 grid. He decided to name this diagram Lo Shu. As the years passed, many mathematicians in different areas studied the Magic Squares. Let's start by talking about the places in general that studied Magic Squares then about the notable mathematicians themselves.
In Persia the actual origin of the Magic Square in the early times is not really known, but some people say
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Divide the original magic square into four squares with equal dimensions.
2. For each smaller magic square defined in step 1, construct a magic square using the odd magic squares construction method, in the order shown in the following figure, from A to D. Each one of those smaller squares contains n2/4 numbers. If A’s largest element is x, B’s smallest element will be x+1, and similarly for B & C, and C & D.
3. Now there are two cases to handle. When n = 6, and when n is a singly even number greater than 6.
a. For n = 6, the numbers highlighted by red need to be swapped with the ones highlighted by blue, as shown in the following figures. For each of these cells, for each singly even number greater than 6, these cells get one cell wider to the right, as shown in the 10x10 magic square in the next part. 6x6 magic square
b. When n is a singly even number greater than 6, an extra swap is needed. The numbers highlighted by purple and bronze need to be swapped. For each singly even number greater than 10, this column gets wider one cell to the left, as shown in the 14x14 magic