Magic Squares

MAGIC SQUARES are really neat. I first encountered them when I was reading about an ancient Chinese astrology called "Nine Star Ki Astrology". This ancient Chinese astrology is related to the I-Ching. If anyone's interested in the Nine Star Ki Astrology, I recommend this book called "An Anthology of I Ching" by W.A. Sherrill and W.K. Chu.

4 9 2
3 5 7
8 1 6
A magic square is a square that contains numbers which sum up, horizontally and vertically, to the same amount. The magic square on the left is the one used in Nine Star Ki astrology. It's called the basic universal table. It also adds diagonally to the same amount as the horizontal and vertical additions. Additionally, the sum of each rows, columns, and diagonals, which comes to 15, when divided by 3 (it's a 3 x 3 square), is 5 which is the number placed in the middle.

The following is the eighty-one magic table produced from the original basic universal table above. It is also part of the Nine Star Ki Astrology. The sum of each rows, columns, and diagonals come to 369, when divided by 9 (it's a 9 x 9 square), is 41 which is the number placed in the middle....

31	76	13	36	81	18	29	74	11
22	40	58	27	45	63	20	38	56
67	4	49	72	9	54	65	2	47
30	75	12	32	77	14	34	79	16
21	39	57	23	41	59	25	43	61
66	3	48	68	5	50	70	7	52
35	80	17	28	73	10	33	78	15
26	44	62	19	37	55	24	42	60
71	8	53	64	1	46	69	6	51

MAGIC SQUARES used in Thai yantras:

The square on the upper right hand corner is a magic square. It contains the following numbers:

1 6 7 4
8 3 2 5
2 5 8 3
7 4 1 6

This square is strange in that the top row and the bottom row contain the same numbers: 1 6 7 4 and 7 4 1 6; and the two middle rows contain the same numbers as well: 8 3 2 5 and 2 5 8 3. These numbers if seen in groups of two, are then listed backward of each other!

The following are two other Thai yantras that contain magic squares:

Magic Squares from "The Kingdom of Siam"

Simon De La Loubere, a French diplomat who came to Thailand in 1687 (Pra Narai's time right before the death of Phaulkon), wrote a book about Thailand called "The Kingdom of Siam" that came to be regarded as "the finest work on seventeenth century Thailand." This book describes the life of Thai people at the time and contains drawings of cultural items like clothing, money, housing, boats, plants, and etc. that came to be included in many history books on Thailand. Curiously, toward the end of this great book, there's a section called "The Problem of the Magical Squares according to the Indians" of which some of the squares I would like to show here:

Magic Squares found in La Loubere's Book:

...

Magic Square in music

Check out these magic square sites:
Magic Squares <----One of the best Magic Squares sites!
Solving Magic Squares
The Determinants of 4 x 4 Magic Squares
Magic Square Algorithm
Susan Alejandre's Magic Squares

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