The Triabolo

The triabolo is an important geometric shape that establishes a connection between two specific Magic Squares.*


THE FOUR TRIABOLOES



THE TRIABOLO OF INTEREST

The above triabolo is the geometric shape that one can find in the 11x11, 19x19 and 27x27 Magic Squares in the Luo Shu format.  



The significance of a  triabolo of numbers in magic squares is that the triabolo is composed of five odd sginificant numbers that, as a group, correspond to a specific magic square.

 

HOW THE TRIABOLO LINKS TWO SPECIFIC MAGIC SQUARES

SIGNIFICANT NUMBERS

5X5

9X9

13X13

              NUMBER LOCATION

components of magic square

2,3

4,5

6,7

 

Odd component of square

3

5

7

         upper right corner cell

Size of square, X

5

9

13

            left of center cell

Center number, Y

13

41

85

                center cell

sum of 1 thru X

15

45

91

           lower right corner cell

X2

25

81

169

            above center cell

sum equals center number of the

61

181

365

                     center cell

corresponding magic square:

11x11

19x19

27x27

   

 

The same triabolo found in these magic squares can also be found in the simple numerical arrangement of numbers in squares.  The size of the square is determined by the odd component of the corresponding magic  square.

CONCLUSION

A.  One Magic Square may correspond to another Magic Square:

The 5x5 Magic Square is connected to the  11x11  Magic Square.
The 9x9 Magic Square is connected to the   19x19   Magic Square.
The 13x13 Magic Square is connected to the 27x27 Magic Square.

B.  The triabolo is another example of how Magic Squares influenced Chinese and Pythagorean numerology. 

Odd numbers were more significant than even numbers in these numerology schemes and enjoyed a higher status.  

Why odd numbers reigned supreme over even numbers:
Only odd numbers can generate Magic Squares in the Luo Shu format and feature a central   number.

Only odd Magic Squares feature a Pythagorean Triad and the numbers of the calendar thereby generating a model for Time and Space.

Only odd numbers can be created by taking the difference of consecutive numbers, squared.

Only triaboloes composed of odd numbers contain the significant numbers of another Magic square, thereby making a correspondence between two magic squares.

All numbers begin with and are created by the first number, one.

* NOTE:  WHEN USING THE TERM MAGIC SQUARE, IT IS MEANT TO MEAN MAGIC SQUARE IN THE LUO SHU FORMAT.