9X9 MAGIC SQUARE

9X9 MAGIC SQUARE

37

78

29

70

21

62

13

54

5

6

38

79

30

71

22

63

14

46

47

7

39

80

31

72

23

55

15

16

48

8

40

81

32

64

24

56

57

17

49

9

41

73

33

65

25

26

58

18

50

1

42

74

34

66

67

27

59

10

51

2

43

75

35

36

68

19

60

11

52

3

44

76

77

28

69

20

61

12

53

4

45

 

This Magic Square is a relationship between 4 and 5, squared

52 - 42 = 9   left of center cell

52 + 42  = 41   center cell

The sum of each row, column, or diagonal is equal to 369

The sum total of all the cells in the square is 3,321

    Pythagorean triads in purple, this is the first Magic Square in the Luo Shu format to have two Pythagorean triads, every higher order Magic Square greater than nine will have two Pythagorean triads in this relative position of the square.

The significant numbers of the 9x9 Magic Square

  number                                 significance                                              location

4                     the even component of the square             upper right corner cell

5                     the odd component of the square          left of lower right corner cell

9                              size,  order of the square                        left of center cell

41                    center number between 1 and 92                        center cell

45                    sum of the numbers one through nine         lower right corner cell

81                    the total numbers in the square                  above central cell          

 

These odd numbers form a triabolo in the 19x19 Magic Square.  The odd significant numbers of the 9x9 magic square add up to 181 (or 92 + 102), the center number of the 19x19 Magic Square.  Therefore, this square is connected to the 19x19 Magic Square.