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Euler and magic squares (De quadratis magicis)

Christophe Hebeisen
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Abstract

Magic squares have always been and are still fascinating for many people, be it only because of their mathematical properties. Their origin is still but certain : we find no magic squares in Greece, and only a 3x3 one in China at the beginning of our era. Most of their development was made in islamic countries. In Europe, Euler wrote two memoirs and numerous pages on magic squares. One of his problems is the famous "officer problem". (In french : Les carres magiques ont toujours fascine la plupart des gens, tant par leur apparente simplicite que par leur etonnante propriete. Leur origine est toutefois assez lointaine et incertaine : il n'y a pas de traces de carres magiques en Grece et on trouve seulement un carre de 3x3 en Chine vers le debut de notre ere. Euler a consacre deux memoires et de nombreuses pages de ses carnets a l'etude des carres magiques. L'un des problemes enonce est le fameux "probleme des officiers".)

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Christophe Hebeisen. 2006-07-20. Euler and magic squares (De quadratis magicis). https://arxiv.org/abs/math/0607468

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