Portraits of Wildflowers

Perspectives on Nature Photography

Archive for June 24th, 2021

Orange-and-yellow and yellow

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If you need your day brightened, here’s some Texas lantana (Lantana urticoides) in a colony of four-nerve daisies (Tetraneuris linearifolia) as I saw them along Yaupon Dr. on June 2nd.


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One thing that can brighten my day is mathematics. In 1514 the great German artist Albrecht Dürer did an engraving called “Melencolia 1.” In the engraving’s upper right corner appeared the following lattice of numbers, the bottom two center cells of which not by chance echoed the year of the engraving:

The numerical lattice that Dürer showed is an example of what mathematicians call a magic square. What’s “magic” about this magic square is that if you add up the numbers in any of the four rows, four columns, or two diagonals, you always get the same total, in this case 34. While the rows, columns, and diagonals add up to a constant in any magic square*, this one is even better because it includes other patterned groups of four cells that also give a total of 34. More than a dozen of them exist. Be the first kid on your block (or in your time zone) to find and point out some of those patterned foursomes that add up to 34. (By “patterned” I mean arranged in an orderly or symmetric way. The set of 5, 7, 9, and 13 wouldn’t count, because although they do add up to 34, the numbers are scattered about in the lattice in no particular way.)

* By tradition, the numbers that fill a magic square are consecutive, with 1 as the smallest number. That needn’t be so, however. For example, you could add 5 to each number in Dürer’s square and the new square would still be magic, except the total in each row, column, and diagonal would now be 54. Or you could double each number in Dürer’s square to get a new square whose magic total would be 68.

© 2021 Steven Schwartzman

Written by Steve Schwartzman

June 24, 2021 at 4:30 AM

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