Nature By Numbers

I’m usually pretty immune to this sort of thing. I don’t want to dazzle my students with math. I want them to engage with math and sometimes the spectacle just intimidates them or makes math seem all the more foreign and unknowable.

Other times the spectacle is simply too spectacular not to share.

I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.


  1. Joe Henderson

    March 27, 2010 - 11:11 am -

    Or, you could ask your students to find some patterns themselves in nature. Just saying…

    Thanks for sharing this. It’s really stunning.

  2. It beats the heck out of my old Powerpoint slideshow with examples of the Fibonacci Sequence in nature.

  3. This video is pretty amazing. Spent some time with some of my kids looking at Phi and body proportions recently. Will be good to use this to provoke a follow up discussion.

    How did you stumble across it? I was looking for ages for something like this, and only found one good video promoting a Christian conference!

  4. I was talking with my student about Fibonacci the other day, and I linked this video to my teacher Facebook account. Comments = 0.

    I talked about 24, and the conversation is still ongoing.

  5. reference the Nautilus shell, which is actually not a golden spiral.

    Last year I was kicking around whether there was some activity where students could do some debunking of golden ratio myths, but I hadn’t worked out a way to present it. This video might be a good start.

    Donald in Mathemagic Land might make more fodder. Here’s a quote from the link above:

    As to the Parthenon, all it takes is more than a cursory glance at all the photos on the Web that purport to show the golden ratio in the structure, to see that they do nothing of the kind. (Look carefully at where and how the superimposed rectangle – usually red or yellow – is drawn and ask yourself: why put it exactly there and why make the lines so thick?)

  6. “Do we know that these examples are measured in nature?”

    I had heard about sunflowers and fibonacci numbers. One day I was taking a walk through a field and came across some sunflowers. I picked one that looked well formed and counted the spirals. Because of the way sunflowers grow, you can either count spirals that go clockwise or counterclockwise. One “direction” (I don’t remember which) will have more spirals than the other.

    Anyway, I counted and was completely floored when it was exactly 34 spirals in one direction and exactly 55 spirals in the other direction. Exactly. I was pretty amazed.

  7. Yeah the sunflowers are very nice. How about that section right after the “construction” of the sunflowers? (Also, are they spread at ~137.5 degrees? which seeds are we picking out?) How are those points picked to create the irregular triangles/hexagons before the perpendicular bisectors are constructed?

  8. I would use this as one piece of evidence that math is beautiful. I’m impressed by the comments and questions posted, and want our students to grasp the pragmatic applications of math, but I also want them to have occasional opportunities, across all curriculum areas, to simply gaze, and experience awe.

  9. Debby: Maybe what makes these scenes so beautiful is that they are utterly pragmatic. The living forms we see today (living and dead) are the results of billions of years of interactions between organisms and their environments in search of solutions to using energy and materials as efficiently as possible given ever-changing conditions. The most pragmatic solutions get to continue passing on their DNA. It’s even been noted that human beauty is highly correlated to facial symmetrical. Symmetry is an indicator of health. We are attuned to recognize beauty because it serves us well whether it be in a potential mate or sunflower.
    Just like we don’t like something because it’s sweet; we like it because sweetness is an indicator that it’s full of energy and thus can keep us alive— we don’t find something beautiful just because it is, we find it beautiful because it promotes life. That’s what attracts us to it.

  10. this would be a great video to show on the first day of school to grab students’ interests. i do my best to connect math to “the real world” and hope to have my students see this connection as frequently and authentically as possible (don’t we all?)

    it’s hard, though, to compete against the level of spectacle our generation receives each day via personal computers and smart phones. i find that many of my students are over-stimulated with gadgets and social networking.

    we must come up with ways to one-up, or at least equal, their other sources of stimulation.