MAGIC SQUARES
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vijay58
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22-02-2010, 09:50 PM


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24-06-2010, 06:09 PM

MAGIC SQUARES
A magic square is a matrix of squares whose
rows, columns and diagonals added up to the same total. a magic square of order n is an arrangement of n^2 numbers in which all rows, all columns, and both diagonals sum to the same constant called the magic constant. The smallest nontrivial case, shown below, is of order 3.n=1 is trivial and doesn't exist for n=2.

History

Chinese mathematicians knew about Magic squares as early as 650 BCE. and Arab mathematicians knew it from the 7th century itself but they learned it from Indian mathematics and astronomy.

Lo Shu square (3×3 magic square)
There is a story about a turtle with a curious figure/pattern on its shell coming out of the flood waters. It had circular dots of numbers which were arranged in a three by three grid pattern such that the sum of the numbers in each row, column and diagonal was the same: 15. This is called the The Lo Shu Square.

Cultural significance
Indian and egyptian civilisations believed that magic squares had astrological and divinatory qualities.

Albrecht Dürer's magic square
The order-4 magic square in Albrecht Dürer's engraving Melencolia I is believed to be the first seen in European art.In this square the rows, columns, diagonals, each of the quadrants, the center four squares, and the corner squares all sum up to 34.

for full details on this topic, visit:
en.wikipediawiki/Magic_square
jonathandimonddownloadables/Magic%20Squares.pdf
combinatoricsVolume_11/PDF/v11i2r2.pdf
combinatoricsVolume_17/PDF/v17i1n8.pdf

search the net for even more details!
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