On magic squares

Details On magic squares On magic squares

2004-08-18

arxiv.org/abs/math/0408230v6

Mathematics

Combinatorics

15 pages, translation of the original Latin ``De quadratis magicis'', Commentationes arithmeticae 2 (1849), 593-602

Scientific paper

This is a translation of Leonhard Euler's ``De quadratis magicis'' . It is E795 in the Enestrom index. This paper studies how to construct magic squares with certain numbers of cells, in particular 9, 16, 25 and 36. It considers some general rules for making squares of even and odd orders. Euler uses Graeco-Latin squares and constrains the values that the variables can take to make magic squares. I think this is where the terms ``Latin'' and ``Graeco-Latin'' square comes from, since he uses Latin letters in one square and Greek (i.e. ``Graeco'') letters in another for each construction. (This paper was published before Euler's only other paper ``Recherches sur une nouvelle espece de quarres magiques'' E530 about Latin squares was, in 1782.)

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