magic squares

Among the "magic" figures, magic squares enjoyed the greatest popularity. These are squares broken into a number of smaller squares, that is, fields, in which the numbers representing some progress are spelled out this way, that the sum of the numbers in each horizontal row and in each vertical column, and there is always one and the same on both diagonals.

Magic squares were known to the Chinese and Hindus for several thousand years. There are Chinese amulets with magic squares, with no digits yet, but there are adequate numbers of punctures or cavities. They were also known to the Arabs in the ninth century of the new era. He introduced them to Europe, or at least the first rules of their lists were shown to Europeans by a Greek named Moscopoulos, who lived in Constantinople in the early 15th century.

The most historic magic square in Europe can be undoubtedly called this one, which appears on one of the masterpieces of the brush D ii r e r a entitled Melancholia. It is a square composed of 16 half, and put together so ingeniously, that the bottom two middle numbers give the year of the work:


And the following centuries, and modern times have not ceased to be interested in magic figures. Great mathematicians, mainly French mathematicians, like Bachet, Fre-nicle, Fermat, Dagger, La Hire, they eagerly develop various methods of putting together magic squares. In his Recreations, Ozanam devotes an entire chapter XII of the first part to them. B. Violle a year 1837 publishes a three-volume work devoted exclusively to magic squares entitled Traite complet des quarres magiąues. Finally, M.. A r n o u x in interesting studies announced in the year 1894, summing up all the achievements of their predecessors, sheds a lot of new and interesting light on this age-old issue.