Dürer and Franklin’s squares
The Lo Shu magic square is well known for its age and uniqueness but one
4×4 magic square has become iconic for its association with a famous artist. It
also has many more properties than some run of the mill magic squares that
make up the 880 different versions. This is the 4×4 square in Albrecht Dürer’s
engraving of Melancholia, which he made in the year 1514.
In Dürer’s square all the rows add up to 34, as do the columns, the diagonals,
and the 2×2 small squares which make up the complete 4×4 square. Dürer even
managed to ‘sign’ his masterpiece with the date of its completion in the middle of
the lowest row.
The American scientist and diplomat Benjamin Franklin saw that constructing
magic squares was a useful tool for sharpening the mind. He was adept at this,
and to this day mathematicians have little idea how he did it; large magic squares
cannot be constructed by serendipity. Franklin confessed that in his youth he had
wasted much time over them despite not being taken with the ‘Arithmetick’ as a
boy. Here’s one he discovered in his youth.