Magic square: Encyclopedia II - Magic square - Brief history of magic squares

Magic square - Brief history of magic squares

Magic square - The Lo Shu Square 3x3 magic square

Chinese literature dating from as early as 2800 BC tells the legend of Lo Shu or "scroll of the river Lo". In ancient China, there was a huge flood. The people tried to offer some sacrifice to the river god of one of the flooding rivers, the Lo river, to calm his anger. Then, there emerged from the water a turtle with a curious figure/pattern on its shell; there were circular dots of numbers that were arranged in a three by three nine-grid pattern such that the sum of the numbers in each row, column and diagonal was the same: 15. This number is also equal to the 15 days in each of the 24 cycles of the Chinese solar year. This pattern, in a certain way, was used by the people in controlling the river.

The Lo Shu Square, as the magic square on the turtle shell is called, is the unique normal magic square of order three.

Magic square - The early squares of order four 4x4 magic squares

The earliest magic square of order four was found in an inscription in Khajuraho, India, dating from the eleventh or twelfth century; it is also a panmagic square where, in addition to the rows, columns and main diagonals, the broken diagonals also have the same sum.

Yang Hui was one of the first mathematicians to study magic squares, or vertical and horizontal diagrams as they were called. He created several magic squares, including 4th order ones. [1]

Magic square - Cultural significance of magic squares

Magic Squares have fascinated humanity throughout the ages, and have been around for over 4,000 years. They were frequently found in a number of cultures, including Egypt and India, engraved on stone or metal and worn as talismans, the belief being that magic squares had astrological and divinatory qualities, their usage ensuring longevity and prevention of diseases.

The Kubera-Kolam is a floor painting used in India which is in the form of a magic square of order three. It is essentially the same as the Lo Shu Square, but with 19 added to each number, giving a magic constant of 72.

The magic square figures in Greek writings dating from about 1300 BC were used by Arab astrologers in the ninth century when drawing up horoscopes. Modern occultism lnks the first 7 magic squares to the 7 traditional astrological planets, as opposed to the astronomical planets of Earth's solar system.

Magic square - Albrecht Dürer's magic square

The order-4 magic square in Albrecht Dürer's engraving Melancholia I is believed to be the first seen in European art. It is very similar to Yang Hui's square, which was created in China about 250 years before Dürer's times. The sum 34 can be found in the rows, columns, diagonals, each of the quadrants, the center four squares, the corner squares, the four outer numbers clockwise from the corners (3+8+14+9) and likewise the four counter-clockwise (the locations of four queens in the two solutions of the 4 queens puzzle [2]), the two sets of four symmetrical numbers (2+8+9+15 and 3+5+12+14) and the sum of the middle two entries of the two outer columns and rows (e.g. 5+9+8+12), as well as several kite-shaped quartets, e.g. 3+5+11+15; the two numbers in the middle of the bottom row give the date of the engraving: 1514.

Magic square - The Sagrada Família magic square

The Passion façade of the Sagrada Família church in Barcelona, designed by sculptor Josep Subirachs, features a 4×4 magic square:

The magic sum of the square is 33, the age of Jesus at the time of the Passion. Structurally, it is very similar to the Melancholia magic square, but it has had the numbers in four of the cells reduced by 1.

Adapted from the Wikipedia article "Brief history of magic squares", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki