Mathpages: Franklin's Magic Squares
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Description: How Benjamin Franklin constructed his magic squares. Autobiographical extract included.
Here's an amusing passage from Benjamin Franklin's autobiography: "Being one day in the country at the house of our common friend, the late learned Mr. Logan, he showed me a folio French book filled with magic squares, wrote, if I forget not, by one M. Frenicle [Bernard Frenicle de Bessy], in which, he said, the author had discovered great ingenuity and dexterity in the management of numbers; and, though several other foreigners had distinguished themselves in the same way, he did not recollect that any one Englishman had done anything of the kind remarkable. I said it was perhaps a mark of the good sense of our English mathematicians that they would not spend their time in things that were merely 'difficiles nugae', incapable of any useful application." Logan disagreed, pointing out that many of the math questions publically posed and answered in England were equally trifling and useless. After some further discussion about how things of this sort might perhaps be useful for sharpening the mind, Franklin says "I then confessed to him that in my younger days, having once some leisure which I still think I might have employed more usefully, I had amused myself in making these kind of magic squares..." Franklin then described an 8x8 magic square he had devised in his youth, and the special properties it possessed. Here is the square: 52 61 4 13 20 29 36 45 14 3 62 51 46 35 30 19 53 60 5 12 21 28 37 44 11 6 59 54 43 38 27 22 55 58 7 10 23 26 39 42 9 8 57 56 41 40 25 24 50 63 2 15 18 31 34 47 16 1 64 49 48 33 32 17 As explained by Franklin, each row and column of the square have the common sum 260. Also, he noted that half of each row or column sums to half of 260. In addition, each of the "bent rows" (as Franklin called them) have the sum 260. The "bent rows" are patterns of 8 numbers with any of the shapes and orientations shown below # - - - - - - - # - - - - - - # - # - - - - - - - # - - - - # - - - # - - - - - - - # - - # - - - - - # - - - - - - - # # -
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