Portraits of Wildflowers

Perspectives on Nature Photography

Orange-and-yellow and yellow

with 18 comments

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.

◊       ◊

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

18 Responses

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  1. Your Texas lantana is a bright light on this dark winter evening.


    June 24, 2021 at 5:22 AM

  2. Little balls of blooms are a challenge for me to photograph; your focus here is so good. The color’s wonderful, too: as hot as the temperatures have been. The photo brought to mind Carmen Miranda, and this.


    June 24, 2021 at 6:31 AM

    • Your mention of good focus on the ball of blooms sent me looking at the photograph’s metadata. I see I managed to get a small aperture, f/16, which accounts for the sharpness of the lantana. At the same time, the four-nerve daisies were relatively far away and therefore showed up as detail-less, non-distracting blobs of color.

      Carmen Miranda immediately got me thinking of Portuguese, and sure enough, the site you linked to is Brazilian.

      Steve Schwartzman

      June 24, 2021 at 6:49 AM

  3. I love this orange and yellow lantana, as opposed to our pink and yellow version. I find the lantana plant all over this property, and appreciate the lovely splash of color, and the fact that the strong scent keeps insects at bay.


    June 24, 2021 at 7:08 AM

    • The pink and yellow lantana, like the all-yellow lantana, comes from outside the United States. The species that’s native in Texas grows wild right in my neighborhood, so I’m fortunate in having it as a photo subject so close to home. I just checked the USDA map and was surprised that Lantana urticoides isn’t shown for a single county in Oklahoma; I’d assumed you’d have it in at least some parts of Oklahoma. As for the scent, if it keeps insects at bay, so much the better; I like the smell in its own right.

      Steve Schwartzman

      June 24, 2021 at 7:21 AM

  4. Indeed your colourful photo brightened my day. Magic squares were one of my students’ favourite activities in my math classes.

    Peter Klopp

    June 24, 2021 at 8:44 AM

    • Then happy brightened day to you after the fact.

      Easy to understand why magic square would be a favorite activity in math classes.

      Steve Schwartzman

      June 24, 2021 at 1:42 PM

  5. We even have lantana up here in Montréal! So pretty!

    Stephanie M

    June 25, 2021 at 8:46 AM

    • Bonjour, Stéphanie, à Montréal. (You could say I saw your one accent mark and raised you two.) Gardeners seem fond of lantanta, even up there in Canada where no lantana species is native. In 2005 I was walking in Australia one morning and was surprised to find some Texas lantana growing in the wild there. Whether it was an escapee from a nearby garden, or whether lantana had hitched a ride to Australia earlier, I don’t know.

      Steve Schwartzman

      June 25, 2021 at 9:01 AM

  6. Lantanas are summer bedding plants here, so it’s interesting to see it growing wild…pretty much the opposite to how I think of it.

    Ann Mackay

    June 25, 2021 at 5:44 PM

    • And of course vice versa for me. I got to know lantana two decades ago as a native shrub in my area.

      Steve Schwartzman

      June 25, 2021 at 7:18 PM

  7. Now that is a background that could stand on its own and a fine one to show off the lantana.

    Steve Gingold

    June 27, 2021 at 2:06 AM

  8. Thought I recognized this flower. I used to purchase a potted variety for some temporary indoor color. (In NJ we had a place called Produce Junction that sold bulk produce and all kinds of flowers at very affordable prices. I miss that place.)


    June 30, 2021 at 11:54 AM

    • Now that the pandemic’s lifting, maybe you could drive over to Produce Junction and bring back a bunch of plants.

      Steve Schwartzman

      June 30, 2021 at 1:33 PM

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