Luoshu was allegedly the first documented "magic square" in the world.
A magic square in mathematics is an array of numbers, in which the numbers in each row, each line and each of the two diagonals have the same sum.
And Luoshu is a 3x3 array of the numbers one through to nine, in which the numbers in each of the three rows, each of the three lines and each of the two diagonals have the same sum of 15.
Chinese mathematician Yang Hui recorded in a book in 1275 some magic squares more complicated than Luoshu, including a 4x4 array of the numbers one through to 16, a 5x5 array of the numbers one through to 25, a 6x6 array of the numbers one through to 36, a 7x7 array of the numbers one through to 49, a 8x8 array of the numbers one through to 64 and a 9x9 array of the numbers one through to 81.
He also made a 10x10 array of the numbers one through to 100, in which the numbers in each of the 10 rows and each of the 10 lines have the same sum of 505, but he failed to make the numbers in each of the two diagonals add up to 505.
It was not until four centuries later that Chinese mathematician Zhang Zhao of the Qing Dynasty (1644-1911) made up a perfect 10x10 magic square.
The first documented magic square in the West was a 4x4 array of the numbers one through to 16. It appeared in a famous print entitled Melancholia, which was created by artist Albrecht Durer in 1514.
Like Luoshu in China, the 4x4 magic square was interpreted in the West as a supernatural sign of order in the universe.
Documents said many Europeans wore amulets bearing patterns of the magic square from the 16th century to the end of World War II (1939-45).
Actually Louis XIV, "le Roi Soleil," was so fascinated by the array that he sent mathematician De La Loubere on a mission to Thailand to learn the way to make a perfect magic square in the 17th century. Loubere arguably invented a method in 1693, with which one can easily make a magic square of odd order of numbers, such as a 9x9 array or an 11x11 one.
(China Daily January 18, 2005)
