Portraits of Wildflowers

Perspectives on Nature Photography

Pi Day

with 47 comments

Some math-minded folks refer to today, 3/14, as Pi Day because 3.14 is the approximate value of π, the ratio of a circle’s circumference to its diameter. In other words, if you could lift a diameter out of a circle, bend it to match the curvature of that circle, then lay it back down onto the circle, it would take about 3.14 such curved segments to go completely around. π is what mathematicians call a transcendental number; one consequence is that we can’t express its exact value with a terminating decimal or even a repeating decimal (as, for example, 1/8 = exactly 0.125 and 1/11 = 0.09090909…).

What’s all that got to do with this opening four-nerve daisy (Tetraneuris scaposa) that I photographed in my neighborhood four days ago? Well, 4 is a number, right? And you’ve gotta admit that the sunny yellow flower head does a good job of suggesting a circle.

© 2019 Steven Schwartzman


Written by Steve Schwartzman

March 14, 2019 at 4:46 AM

47 Responses

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  1. Wow! That was a lot to take in this early in the day. My brain hurts now. I remember having to set pi on my very expensive slide rule to work out circumferences or some such thing. I was, and still am, better with numbers than geometry or trigonometry. Nice circle though 😀


    March 14, 2019 at 5:20 AM

  2. Interesting. Brings to minds the closing paragraphs of Sagan’s novel “Contact.”


    March 14, 2019 at 5:41 AM

    • I “contacted” a synopsis of that novel to see what you were referring to. Let’s hear it for numbers!

      Steve Schwartzman

      March 14, 2019 at 6:57 AM

  3. I like pie for breakfast

    For want of an E
    A pie was lost
    For want of an A
    Toast was tossed
    For want of Time
    A waffle was defrost
    For want of a Brain
    Did this rhyme exhaust

    Robert Parker

    March 14, 2019 at 5:47 AM

    • By now I hope your breakfast is brokefast.

      With the dropping of an e
      What I wanted to hide got hid,
      What I wanted to slide got slid,
      And now to you adieu got bid.

      Steve Schwartzman

      March 14, 2019 at 7:08 AM

  4. Every now and then, my dad would say to me, “Pi r square.” Then, in a fit of giggles, I’d give the expected response. “No, pie aren’t square. Pie are round. Cake are square.”


    March 14, 2019 at 7:39 AM

    • I’ve heard that one but didn’t realize how far back it goes. Circles have been a-round for a long time.

      Steve Schwartzman

      March 14, 2019 at 7:48 AM

      • I heard an interview this afternoon with Emma Haruka Iwao, who now owns the world record for calculating pi — to something like 31 trillion digits. She works for Google, and used cloud computing to achieve her record. When the interviewer asked how she celebrated, she said she and her co-workers shared apple pie.


        March 14, 2019 at 4:56 PM

        • That’s a good story, and one that aired today for an obvious reason. 31 trillion is a lot of digits.

          Steve Schwartzman

          March 14, 2019 at 6:21 PM

  5. And a little sun pie. Aw, adorable! Thanks for reminding me to take my math loving son out for a pie today!


    March 14, 2019 at 9:17 AM

    • And while you’re taking him out for that confection, preferably pie-napple, you might also see a magpie.

      Steve Schwartzman

      March 14, 2019 at 9:50 AM

      • Oh, if only. We had magpies in Sacramento when we lived there and I grew quite fond of them.


        March 16, 2019 at 8:45 AM

        • We might almost say you made a sacrament of them there.

          Steve Schwartzman

          March 16, 2019 at 11:48 AM

          • Yes. I believe I made a Sacrament of everything In California. If I were rich and California the same as I remember it, I’d hie me back. Alas….


            March 17, 2019 at 8:04 AM

            • Good word, hie.

              Steve Schwartzman

              March 17, 2019 at 9:33 AM

              • I always thought so.


                March 18, 2019 at 9:57 AM

                • I suspect few people know that word now.

                  Steve Schwartzman

                  March 18, 2019 at 9:49 PM

                • It saddens me, the downward trajectory of our level of education. I went to school in a pretty backward little town, yet had topnotch teachers. It must have broken their hearts to see the bulk of students willfully refuse to learn. When I pick up a library book these days, I’ve found increasingly poor grammar and incorrect word usage. That tells me the authors AND the so-called editors are illiterate!


                  March 20, 2019 at 9:59 AM

                • For ideological reasons, the people in charge of education just will not allow failure. If too many kids would fail because they haven’t put in the time and energy to learn what they’re supposed to, then the people in charge lower the standards to guarantee that almost everyone will pass. It’s a bigger scandal than the one currently in the news because it affects millions of kids, not a few hundred.

                  Steve Schwartzman

                  March 20, 2019 at 11:15 AM

                • That’s true. I’m remembering my son mentioning that there was no incentive to try in school, because they all knew they’d “pass” anyway, and better grades were just too easy to get.


                  March 21, 2019 at 10:05 AM

                • Yup, that’s how bad things have become, alas.

                  Steve Schwartzman

                  March 21, 2019 at 8:51 PM

                • Perhaps they skipped college. Or perhaps their mommies paid $500,000 to get them in just so they could party.


                  March 20, 2019 at 10:00 AM

  6. “… it would fit around the circle about 3.14 times.”

    Can I suggest a little wordsmithing here? I interpret that phrase to mean that a SINGLE diameter lifted from the circle would wrap around the circle 3.14 times. You and I both know that’s not right. It would take (approximately) 3.14 diameters to wrap the entire circle ONCE.


    March 14, 2019 at 11:47 AM

    • I agree that your wording is better. Mine was at best ambiguous. I’d intended to use a phrase like “if put end to end” but it got left out. I’ve reworded the text. Thanks.

      Steve Schwartzman

      March 14, 2019 at 3:48 PM

  7. I’d say you picked a perfect Pi !!


    March 14, 2019 at 6:28 PM

  8. Transcendental? And I thought that pi was merely irrational. Beautiful light in your image of the daisy.


    March 15, 2019 at 10:45 PM

    • Transcendental is a more restrictive category. All transcendental numbers are irrational but not all irrational numbers are transcendental. For example, the square root of 5 is irrational but not transcendental. Transcendental numbers transcend the ability to be expressed as finite combinations of roots. You can find more detail at


      Steve Schwartzman

      March 16, 2019 at 5:47 AM

      • Reading the definition, I realized that computing pi must be a matter of approximation, since you can’t express pi algebraically. I just browsed through the history of computing pi on Wikipedia.


        March 16, 2019 at 9:09 AM

        • You’re correct. It’s just a question of how many decimal places one needs—or more likely wants. As you read, mathematicians have gone out zillions of places to try to answer questions like whether each digit in the infinite expansion occurs approximately equally often.

          One early mathematical discovery was that this very simple infinite series converges to π/4:

          1 – 1/3 + 1/5 – 1/7 + 1/9 – 1/11 + ….

          The problem is that the series converges very slowly and is therefore not a practical way to calculate π.

          Steve Schwartzman

          March 16, 2019 at 11:56 AM

          • The history of computing pi seems to come down to: (1) how many decimal places, and (2) the speed of the convergence (effciency). I read little about how you validate an approximation, that might be tricky given the precision (in decimal places) of calculations on computers.


            March 17, 2019 at 8:40 PM

            • Like you, I don’t know how mathematicians get computers to carry out the calculations. I imagine one way to check for errors is to calculate the value of π by two or more different methods and compare the results.

              Steve Schwartzman

              March 17, 2019 at 9:58 PM

  9. In Santa Cruz, April 20 is designated as Weed Day because 420 is the number of the legislation that legalized marijuana. Pi Day doesn’t sound so far fetched.


    March 16, 2019 at 6:39 PM

    • I think Pi Day came about before Weed Day. In fact after writing that I checked and found at


      that “In 1988, the earliest known official or large-scale celebration of Pi Day was organized by Larry Shaw at the San Francisco Exploratorium, where Shaw worked as a physicist, with staff and public marching around one of its circular spaces, then consuming fruit pies.”

      Steve Schwartzman

      March 16, 2019 at 10:03 PM

      • How amusing that it was at the Exploratorium, where they are experts on circular spaces. I remember that the big rotunda there is designed with the focus of the large dome right above floor level, so ‘everything’ within the rotunda can be heard be standing in the middle of the floor. Seriously, I could hear every little pigeon noise in the rotunda, and every footstep of the few people who walked in. San Francisco is just about fifty miles from the Santa Clara Valley, where we are experts on fruit pies! Some people might have been aware of that in 1988, not that it was important in San Francisco.
        Weed Day happened in only the past few years. It is not something we are proud of here.


        March 17, 2019 at 7:42 PM

        • People have built so-called whispering galleries in several places. When I taught precalculus we studied the conic sections—hyperbolas, parabolas, and ellipses (which include circles)—and some of their interesting properties. While we learned about π, I don’t think we ever studied fruit pies. Maybe in the Santa Clara Valley we would have.

          Steve Schwartzman

          March 17, 2019 at 10:05 PM

  10. It would be a shame to lift three diameters out of this pretty little daisy to prove that they would approximately add up to the circumference of its circle, so we will take your word for it.


    March 17, 2019 at 9:26 PM

  11. Math was definitely not one of my better subjects! Speaking of the latter, that sure is a gorgeous daisy 🙂


    March 19, 2019 at 8:50 PM

    • It’s a daisy that’s not only common here but one that can be found flowering for much of the year.

      Steve Schwartzman

      March 19, 2019 at 10:03 PM

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