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Science Frontiers ONLINE No. 110: Mar-Apr 1997 |
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Alphamagic Squares
Not everything in SF is profound or anomalous, although we hope most of the items are at least interesting.
Magic squares, we think, are endlessly fascinating. They exist in forms that verge on the unbelievable. You can even construct large magic squares from smaller magic squares. Nevertheless, the fact that alphamagic squares exist in large numbers is unexpected.
Alphamagic squares come in pairs. The first member of the pair consists of a magic square in which the numbers are spelled out letterwise, as in this example:
| five | twenty-two | eighteen |
| twenty-eight | fifteen | two |
| twelve | eight | twenty-five |
The numbers add up to 45 in all rows, columns, and diagonals. The square is "magic" in words.
The second member of the pair is formed by counting the number of letters in each word of the first square, thus:
| 4 | 9 | 8 |
| 11 | 7 | 3 |
| 6 | 5 | 10 |
This square is also magic, adding up to 21 in all directions!
Just a fluke, you say? Not so. You can even construct alphamagic squares in different languages. In his column in Scientific American, I. Stewart provides examples in French, German, Welsh, and even Swahili! In German, there are no less than 221 alphamagic squares using numbers under 100.
(Stewart, Ian; "Alphamagic Squares," Scientific American, 276:106, January 1997.)
Comment. The "deep meaning" of alphamagic squares is about the same as that associated with the existence of your Social Security Number in the decimal expansion of pi!