Discussion of 13x13 MAGIC SQUARE

EXAMPLE: 13x13  Magic Square

The number 13 is represented by the 13x13 Magic Square. That is, a square that is 13 columns by 13 rows which will yield 169 (or 13 squared) numbers or cells. Arranging the numbers 1 thru 169 in a square in the Luo Shu format begins to reveal a repeatable pattern involving the same numbers (1, 7, 13, 85, 91, 169).

By definition of the Luo Shu format, this square is a relationship between six and seven, squared. Subtracting these numbers   (49 - 36) will yield 13 and adding these numbers (49 + 36) will yield 85, the most important number of the 13x13 Magic Square because it occupies the center cell and the center axis of the square.

The product of 13 and 85 equals the constant of the cell, 1105. And the product of 13 squared and 85 equals the sum total of all the numbers in the 13x13 magic square: 14,365 - a number that is connected to the 27x27 magic square. 

13 and 14 are the basis for the 27x27 magic square with 365 as the center cell.  Following the numbers 7, 13, 85, 91, and 169 in both squares reveals the numbers of the calendar.  Several right angle triangles are also present in the 27x27 magic square.  These squares are  examples of the association of the Luo Shu with Time and Space.  Time as in the numbers of the calendar and Space as in the Pythagorean Theorem.

Most interesting is the triabolo that appears in the 27x27 Magic Square.  A triabolo is a geometric figure composed of three right angle triangles.  The triabolo in the 27x27 Magic Square involves the numbers of the calendar (7, 13, 85, 91, and 169) in such a way that when doing some simple arithmetic generates the numbers 1, 13, and 14. 

In the 13x13 Luo Shu Magic Square, a diabolo is formed with the numbers 7, 72, 85, and 91.  And the numbers 13 and 169 are positioned next to 85 and are part of the 13, 84, and 85 Pythagorean Triad.

In the Lo Shu format, all odd Magic Squares will follow this format:

  1. The center cell is represented by the middle number of the total numbers in the square, and is the most important number in the square, in this case 85.
  2. The cell to the left of the center cell represents the order or size of the square, in this case 13 (the seventh odd number).
  3. The cell above the cell that represents the order of the square together with the center cell and the cell left of the center cell form a Pythagorean triad of numbers, represented by green numbers in the above 13x13 magic square.
  4. The cell above the center cell represents the highest number in the square, in this case 169. 
  5. The cell in the lower right corner represents the sum of 1 through the number of the order of the square. For example, for the 3x3 Magic Square, 1 + 2 + 3 = 6, and six goes in the lower right corner cell of the square.  In the 13x13 Magic Square, 91 is the sum of the first thirteen numbers and occupies the lower right corner cell of the square.
  6. The cell to the left of the lower right corner cell represents the lesser of the two consecutive numbers the square is based on, in this case 6.
  7. The cell in the upper right corner represents the greater of the two consecutive numbers the square is based on, in this case 7.
  8. One is always placed below the center cell and any size magic square can be constructed starting here.