Lo Shu turtleMagic Squares can be traced in Chinese literature as far back as 2800 B.C. The legend of "Lo Shu" or "scroll of the river Lo" tells the story of a huge flood that destroyed crops and land. The people offered a sacrifice to the river god for one of the flooded rivers, the Lo river, to calm his anger. Everytime the river flooded, there emerged a turtle that would walk around the sacrifice. It was not until a child noticed a unique pattern on the turtles shell (Figure 2) that told the people how many sacrifices to make for the river god to accept their sacrifice. There were circular dots of numbers that were arranged in a 3-by-3 grid pattern such that the sum of the numbers in each column, row, and diagonal equaled the same sum: fifteen. Fifteen became the number of sacrifices needed in order to make the river god happy. This number is equal to the number of days in each of the 24 cylces of the Chinese solar year.

Diabolic squareThe oldest magic square of order four was found inscribed in Khajuraho, India dating to the eleventh or twelfth century. This magic square is also known as the diabolic or panmagic square, where, in addition to the rows, columns, and diagonals the broken diagonals also have the same sum. The magic square at the right shows an example of a diabolic or magic square.

Magic Squares have been around for over 4,000 years and have been used in different cultures for their astrological, divinatory qualities, their usage ensuring longevity and prevention against diseases. For example, Indian and Egyptian cultures engraved magic squares onto stone or metal into gowns worn by talismans.


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