The Luo Shu - 3x3 Magic Square

A magic square is defined as an arrangement of numbers in a square such that the numbers of any given row, column, or diagonal will add up the same number, known as the constant of the square.

The simplest and smallest magic square is the 3x3 Magic Square, known as the Luo Shu.

Magic squares in the Luo Shu format will have specific features as these squares are based on the following formula:

4	9	2			Y - 1	X2	Y - X
3	5	7			X	Y	2Y - X
8	1	6			X + Y	1	Y + 1

This square is based on the first two consecutive integers, 1 and 2

2² – 1² = 3           THE SIZE OR ORDER OF THE SQUARE               X

2² + 1² = 5         THE CENTER NUMBER OF THE SQUARE = (X²+1)/2 = Y

3*5 = 15                THE CONSTANT OF THE SQUARE                  X*Y

3²5 = 45                THE SUM TOTAL OF ALL THE NUMBERS          X²Y

    A Pythagorean  triad of numbers always occurs in this position of any magic square in the Luo Shu format.

The Significant Numbers of the Square

1   represents the lesser of the two consecutive numbers that are the components of the square this number is always to the left of the lower left corner cell of the square

2   represents the greater of the two consecutive numbers that are the components of the  square this number is always in the upper right corner cell of the square

3   represents the size of the square and this number is always to the left of the center cell

5   represents the center number between 1 and X² , or in the above case, 1 – 9

6   represents the sum of all the integers 1 thru X, or in the above case 1 + 2    + 3, this number is always placed in the lower right corner cell of the square

9   represents the total numbers in the square and is equal to X² , or in the above case 3² , this number is always placed above the center cell