See the node magic square for a definition of the term.
1   15  14  4

12  6   7   9

8   10  11  5

13  3   2   16
This magic square consists of consecutive numbers from 1 through 16. Adding any horizontal row, vertical column, or diagonal will result in a sum of 34. This square was popular in the 16th century, when Europeans thought it to have the power to ward off plague and disease. The background of Albrecht Durer's famous "Melencolia I" engraving (1514) contains a very similar square. The square is still quite popular in various parts of Eastern Asia.
4 9 2

3 5 7

8 1 6
The oldest known magic square, this example dates back at least 4000 years and can be found in the I Ching. Various incarnations of the square can be found throughout ancient history. A powerful mystical symbol to the Chinese, this particular square also represented the name of God to the ancient Hebrews. The first two letters of the name of God, YH, represent the number 15. All rows, columns, and diagonals in the square have a sum of 15.

During the Middle Ages, magic squares came to represent various planets. The 16-number square above was Jupiter, whereas the 9-number one represented Saturn. Among the secrets thought to be held by the squares were methods for turning various metals into gold and tracking astronomical bodies.

The magic square,

4 9 2
3 5 7
8 1 6

played an important part in the development of mathematics in ancient China. Legend has it than an Emperor Yu recieved this magic square from a Lo River Tortoise. It was part of a series of diagrams called the Lo Shu which contained the foundations of Chinese mathematics.

The important thing about this particular magic square is it led to the devolopment of dualistic theory, ie. Yin and Yang, where Yin is represented by the even numbers and Yang by the odd numbers. Notice how the even and odd numbers are distributed within the square, somewhat like a Yin Yang, in the sense of an even distribution.

Thanks to Falsch Freiheit for pointing out to me how the square also resembles a yin yang with one color being represented by numbers less than five, and the other by numbers greater than five. He says: "4, 3 and 1 are the 'body' of one side, with 8 as the dot in the center, 9 7 6 the 'body' of the other side with 2 the dot in the center." I suppose the five is simply the border between the two bodies.

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