Portraits of Wildflowers

Perspectives on Nature Photography

Another snagged feather

with 26 comments

Small White Feather Caught on Dry Grass Stalk 1348A

While I wandered along Brushy Creek near Parmer Ln. on February 21st in the town of Cedar Park, I noticed—not for the first time and not for the last—a small feather that had gotten caught on something, in this case a dry grass stalk. I think the photograph’s overall blue cast is due to the fact that the scene was largely in the shade of the trees that you can make out indistinctly in the background.

I’d originally planned to show this picture in a conventional rectangular cropping, but March 14th, 3/14, happens to be π Day. You’ll recall that π, whose value is about 3.14, is the ratio of the circumference of a circle to its diameter. In other words, if you take a diameter of a circle, bend it to match the curvature of the circle, and lay that curved diameter successively around the circumference, it will fit approximately 3.14 times.

It may surprise you to learn that π turns up in many places that seemingly have nothing to do with circles. How, you wonder, is that possible? Now that I have your rapt attention, let me give you an example. Suppose you have a hardwood floor in one of your rooms, and let’s say that the long planks of wood are 4 inches wide. Imagine you take a 4-inch-long needle and repeatedly toss it onto the wooden floor. More often than not the needle will come to rest touching one of the parallel cracks between the rows of boards. Sometimes, though, the needle will end up in such a way that it’s entirely on a board and doesn’t touch the crack on either side. What are the chances that a tossed needle will touch one of the cracks? It turns out that the chances are 2/π. If you divide 2 by π, you’ll see that that amounts to about 0.637; in other words, if you repeatedly toss a needle that’s as long as the boards are wide, then in the long run the needle will end up touching a crack between the rows of parallel boards about 63.7% of the time.

If you’d like to learn more about this question, which has been called the Buffon needle problem, you can read various articles about it. And while we’re being brainy today, you might also be interested to know that 3/14 was the birth date of Albert Einstein (in 1879).

© 2014 Steven Schwartzman

Written by Steve Schwartzman

March 14, 2014 at 6:00 AM

26 Responses

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  1. thanks for this, the photo and the math titbits. numbers make the world go round!


    March 14, 2014 at 7:13 AM

    • What a good way to reply to a post that includes math and a circle: “numbers make the world go round!”

      Steve Schwartzman

      March 14, 2014 at 7:22 AM

  2. A beautiful feather. The Comte de Buffon seems to have snagged an entire bird as he sits in the Jardin des Plantes. http://farm5.staticflickr.com/4123/4917331085_b9026af59a_o.jpg


    March 14, 2014 at 7:40 AM

  3. When I first glimpsed the cropping, I suspected you’d served up some Pi for us. It tickled me you found such a creative way to do it — feather and all.

    Of course, your blog has something else in common with Pi – its value is constant.


    March 14, 2014 at 8:43 AM

    • What an excellent insight in that last sentence! Thanks.

      Because I didn’t mention π Day last year or the year before, I thought I should say something this time around—with emphasis on around.

      Steve Schwartzman

      March 14, 2014 at 12:44 PM

  4. Happy π day, Steve! : )


    March 14, 2014 at 1:59 PM

  5. When I was a nerdy kid (in the days before I became a nerdy adult) one of the ways I’d amuse myself was by calculating π. This was pre-calculator.

    The last time I played basketball my jersey number was π.


    March 14, 2014 at 7:18 PM

    • Nerds of the Internet, unite! I’ve heard of people calculating the value of π , but to hear of a person (you) wearing that number on a basketball jersey is something new.

      Steve Schwartzman

      March 14, 2014 at 7:49 PM

  6. […] Texas wildflowers. I recently started using his photography tips in my nature shots. Yesterday he blogged about March 14 being π day (3.14 day). i love numbers and math(s) so i was intrigued to find out more about the […]

  7. Is this where I admit that the most mathematical I get is to head for Baker’s Square to round out my day with pie?


    March 15, 2014 at 10:47 AM

    • Except that from having read this you’re a little more mathematical than you were before. You remind me of the old joke in which a teacher gives the formula for the area of a circle, π r squared, to which a student replies: no, pie are round.

      Steve Schwartzman

      March 15, 2014 at 1:32 PM

  8. I do love the photo!


    March 15, 2014 at 10:47 AM

    • I’m glad you do, Melissa. I’ll add that photographing the feather was hard because the slight breeze caused it to keep moving around and I had trouble getting a good composition with the main parts of the feather in focus.

      Steve Schwartzman

      March 15, 2014 at 1:39 PM

  9. What a great post, thanks for sharing.

    Emma Sarah Tennant

    March 17, 2014 at 11:47 AM

  10. As you know only too well, I am far more likely to have a Buffoon problem when it comes to any sort of math. Good thing there are folk like you around to solve those sorts of things!


    March 17, 2014 at 2:21 PM

    • And it’s good that there are people like you around who enjoy playing with words. That beats playing the buffoon.

      Steve Schwartzman

      March 17, 2014 at 2:24 PM

  11. Leave it to a mathematician! I’ll have to check out the links for the resolution of this problem seems counter intuitive … at least regarding its derrivation … I mean, come on, 2/π … who would a thunk it? Thanks for putting just-one-more-thing into my (very) limited head space space. D

    Pairodox Farm

    March 19, 2014 at 12:50 PM

    • The equation for the basic bell curve (standard normal distribution) also contains π. Mathematicians are pied pipers, calling everyone to follow the enchantment.

      Steve Schwartzman

      March 19, 2014 at 2:46 PM

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