Portraits of Wildflowers

Perspectives on Nature Photography

Visiting nerve-ray

with 27 comments

On the first day of May this Tetragonotheca texana (known by the strange name nerve-ray) had two simultaneous morning visitors. Whether the non-me visitor was a non-bee. i.e. a bee-fly, I’m not sure. Nerve-ray is one of the few yellow daisy-type flowers that’s fragrant. Where the conventional wisdom is to stop and smell the roses, I always stop and bend down to enjoy the subtle fragrance of nerve-ray flowers.

Another colloquial name for nerve-ray is square-bud daisy. The starkly lit portrait below explains that name.

I’ll grant you that this bud looks a bit off from being exactly square—hey, nature’s not perfect. For that matter, neither is language. As nice and succinct as square is, English doesn’t have a simple word to designate ‘any four-sided closed figure in a plane.’ English has occasionally used Greek-derived tetragon, following the same pattern in the familiar pentagon and hexagon. Nowadays, though, English is pretty much stuck with the unwieldy five-syllable Latin-derived quadrilateral. If only we could follow the model of German, a related language, which has Viereck, literally ‘four-edge(s),’ and call a quadrilateral a fouredge or a fourside.

Speaking of quadrilaterals, here’s something interesting you may not know, or if you did learn it in high school geometry have probably forgotten. Take any quadrilateral you like, whether convex, concave, or even with two of its sides crossing each other. Connect the midpoints of the four sides (going in order from each side to the next) with straight line segments and you’re guaranteed to end up with a parallelogram. That’s just how the universe is. As a picture is often worth a lot of words—some say a thousand, others a myriad—you’re welcome to look at an example with a convex quadrilateral.

© 2021 Steven Schwartzman


Written by Steve Schwartzman

May 11, 2021 at 4:32 AM

27 Responses

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  1. It does appear to be a bee-fly but which one it be? Nice to have company.

    Steve Gingold

    May 11, 2021 at 5:01 AM

    • That there be bee-flies flies in the face of what many believe to be the case, but that may be better than facing one flying in their real face.

      Steve Schwartzman

      May 11, 2021 at 6:55 AM

      • LOL, that would make an excellent tongue twister… 🙂

        Ann Mackay

        May 11, 2021 at 10:15 AM

  2. I think it’s a syrphid fly.

    Alessandra Chaves

    May 11, 2021 at 8:09 AM

  3. I never see a nerve-ray bud without thinking of Dim Sum: particularly, the steamed pork buns ((Char Siu Bao).
    I’m sure that little pollinator thinks the flower is just as delicious.

    I’m actually rather fond of ‘quadrilateral’ as a word. I like ‘quadruple’ and ‘quarto,’ too. There’s just something about the sound that appeals. It was interesting to find a relationship with ‘quarrel’ — not as an argument between people, but as a “short, heavy, square-headed, four-edged bolt or arrow for a crossbow.” It’s always fun to go down the etymological rabbit holes.


    May 11, 2021 at 8:41 AM

    • Down those etymological rabbit holes it where you’ll often find me. Speaking of which, the second word in Welsh rarebit is seemingly an altered form of rabbit. And the quarrel that you mentioned apparently consists of the same etymological elements as quadrille.

      Your char siu bao sent me down a time tunnel rather than a rabbit hole. At the Chinese restaurant in the town where I grew up we often ordered char siu ding.

      Steve Schwartzman

      May 11, 2021 at 3:33 PM

  4. I agree with comments above, this is probably a syrphid fly. I’ve seen them here, too.

    I have bookmarked the geometry site. Thanks!

    Lavinia Ross

    May 11, 2021 at 9:50 AM

    • I’m always happy to see syrphid flies. Could it be because the word reminds me of syrup? At your leisure you can enjoy the sweet geometry you’ve bookmarked.

      Steve Schwartzman

      May 11, 2021 at 3:36 PM

  5. Gorgeous macro, Steve! I’ve never seen that flower!


    May 11, 2021 at 11:34 AM

    • I’m not surprised you haven’t seen it. Fortunately it’s pretty common in my part of Austin.

      Steve Schwartzman

      May 11, 2021 at 3:47 PM

  6. The beauty and fragrance of the nerve-fly flower immediately attracted Madame Pollinator.

    Peter Klopp

    May 11, 2021 at 12:13 PM

  7. I took a quick look at the maths but my mind slid off it. It is not good with such things.

    I loved the square bud. It reminded me of a balloon flower bud, but obviously more square. 🙂


    May 11, 2021 at 3:22 PM

    • I had to look up balloon flower. One site says: “Children love to grow this plant for the balloon-like buds which pop when squeezed.” It never occurred to me to try squeezing a nerve-ray bud; maybe it would pop, too.

      Even if you don’t follow the proof given in that link, you can still appreciate the reality of the relationship. If you’re willing, get a pencil, a ruler, and a piece of blank paper. Use the pencil and ruler to draw any random quadrilateral you like. Use the ruler to measure each side and mark each side’s midpoint. Then use the ruler and pencil to connect each midpoint to the next until you’re back where you started. You’ll see that you just drew a parallelogram.

      Steve Schwartzman

      May 11, 2021 at 3:59 PM

      • I’ve just been drawing it out Steve. Essentially you are saying there is no way to join the points so that they make a square?


        May 12, 2021 at 2:22 PM

        • No matter the shape of the quadrilateral you start out with, connecting the midpoints of the sides is guaranteed to create a parallelogram. Differently shaped starting quadrilaterals will yield differently shaped parallelograms.

          A square is a special kind of parallelogram; what makes it special is that not only are opposite sides parallel, which is true in any parallelogram, but in addition all the sides of a square are equal and all the angles are 90°.

          If the quadrilateral you start with happens to be a square, connecting the midpoints will give you another square.

          Steve Schwartzman

          May 12, 2021 at 4:53 PM

          • I was forgetting that a square is a parallelogram. I have been laughing since getting your answer, thinking of how you would grade my response. I used to like maths at school, and still find it interesting at some level, but the intervening years have not helped.


            May 12, 2021 at 5:27 PM

            • One thing is certain: none of us remember all the things we once knew. Sic transit gloria mundi.

              Steve Schwartzman

              May 12, 2021 at 6:51 PM

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