The ancient Chinese Magic Square was followed by the Lo Shu Square, which dates back to 2200 B.C. It symbolizes the natural order of the Universe, promoting logic, strategy and open-mindedness.
The Legend of Lo Shu
During ancient times in China there was a huge flood on the Lo River. The people tried to calm the River god’s anger by offering sacrifices, but each time they prepared an offering a turtle came up from the river and walked around the sacrifice, and the River god wouldn't accept the sacrifice. This happened several times, until one time, a child noticed curious markings forming a pattern on the turtle’s shell. After studying these markings the people realized the correct amount of sacrifices to make, that is 15. Then the river god was placated. The numbers in every row, up and down, across, or diagonally, add up to 15, which happens to be the number of days it takes for the new moon to become a full moon.
The odd and even numbers alternate in the periphery of the Lo Shu pattern; the 4 even numbers are at the four corners, and the 5 odd numbers (outnumbering the even numbers by one) form a cross in the center of the square. The sums in each of the 3 rows, in each of the 3 columns, and in both diagonals, are all 15 (the number of days in each of the 24 cycles of the Chinese solar year). Since 5 is in the center cell, the sum of any two other cells that are directly through the 5 from each other is 10 (e.g., opposite corners add up to 10.
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 in which 1 is at the bottom and 2 is in the upper right corner. Every normal magic square of order three is obtained from the Lo Shu by rotation or reflection.
The Square of Lo Shu is also referred to as the Magic Square of Saturn or Chronos.
Cultural significance of the magic square in India
Magic squares have fascinated humanity throughout the ages, and have been around for over 4,120 years. They are 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.
23 28 21
22 24 26
27 20 25
The 3x3 magic square was used as part of rituals in India from vedic times, and continues to be used to this day. The Ganesh yantra is a 3x3 magic square. A well known early 4x4 magic square in India can be seen in Khajuraho in the Parshvanath Jain temple. It dates from the 10th century.
7 12 1 14
The 3x3 magic square was used as part of rituals in India from vedic times, and continues to be used to this day. The Ganesh yantra is a 3x3 magic square. A well known early 4x4 magic square in India can be seen in Khajuraho in the Parshvanath Jain temple. It dates from the 10th century.
7 12 1 14
2 13 8 11
16 3 10 5
16 3 10 5
9 6 15 4
This is referred to as the Chautisa Yantra, since each row, column, diagonal, 2x2 sub-square, the corners of each 3x3 and 4x4 square, the two sets of four symmetrical numbers (1+11+16+6 and 2+12+15+5), and the sum of the middle two entries of the two outer columns and rows (12+1+6+15 and 2+16+11+5), sums to 34. And Chautisa in Hindi means 34.
This is referred to as the Chautisa Yantra, since each row, column, diagonal, 2x2 sub-square, the corners of each 3x3 and 4x4 square, the two sets of four symmetrical numbers (1+11+16+6 and 2+12+15+5), and the sum of the middle two entries of the two outer columns and rows (12+1+6+15 and 2+16+11+5), sums to 34. And Chautisa in Hindi means 34.
