Getting Mathematical on Weeds.

Dandelions amaze me.

We tend to take them for granted.

“Huh.  They’re just stupid weeds. ” , many of us might say.

But if you look closer, they’re actually quite beautiful.

And if you zoom in REALLY close, you’ll find something even more amazing.

Notice, there’s definitely a spiral pattern there.

If you connect the dots, you can definitely count 13 curves in the clockwise direction.

But if you connect the dots in a counter-clockwise direction, you get 21 curves.

Now, remember those numbers, (13 and 21), while I digress for a bit.

Consider this mathematical sequence of numbers.

0,  1,  1,  2,  3,  5,  8,  13,  21,  34,  55,  89….

For those of you who don’t recognize this,   these are Fibonacci numbers, where any given number is the sum of the previous two.

It’s quite simple:

0 + 1 = 1

1 + 1 = 2

1 + 2 = 3

2+ 3 = 5…and so on.

Now, if you draw a series of squares,  based on the Fibonacci sequence, and you get something like this:

And if you draw a continuous arc though each square,  it forms a spiral seashell pattern, like this:


This is called the Fibonacci Spiral

Now, let’s take my 13 clockwise red-curves:

And if I take them, one by one, and superimpose them on the Fibonacci Spiral, I get this:

Kinda fits, doesn’t it?

Same thing if I take the 21 counterclockwise curves…

Again, each curve also seems to fit, when superimposed  on the counter-clockwise Fibonacci spiral:

Now, let’s just recap:

I zoomed in on a photo or a dandelion, connected dots and generated some rough curves.

And the shape of these curves fit a spiral based on the Fibonacci sequence.

Not to mention, the number of clockwise and counter-clockwise spirals are 13 and 21.
Which are Fibonacci numbers themselves.

What’s going on here?   Is this magic?   Or  a fluke?


Actually, this is no accident.

You see, Nature tends to like Fibonacci numbers.   For example, you rarely see flowers with 4 or 6 petals.  But you see many with 3, 5 or 8.

Flowers seed pods are also arranged this way.  The number of spirals are always Fibonacci numbers…one clockwise, one counter-clockwise.

In this case, with my dandelion,  it was 13 and 21.  With larger flowers (like Sunflowers), you’ll find numbers 34 and 55.

But why Fibonacci numbers?

Basically, it has to do with Nature trying to optimize itself.  With flowers, if seeds are arranged in Fibonacci spirals, you can fit more of them onto the plant,  and you get more bang for your buck.    There’s a good interactive exercise that demonstrates this.

I won’t get into the whole mathematical explanation.   But you can find some good discussions here and here.

It’s not just dandelions.  You’ll also find Fibonacci sequences with pine cones, pineapples and asparagus and seashells.       Plant leaves are arranged in Fibonnacci spirals, to optimize the sunlight they recieve.

Fibonacci numbers are everywher in Nature   More examples are shown here.


It’s pretty amazing, when you think about it.

Take an abstract concept.   A sequence of pure, unadulterated numbers:

0, 1,  1,  2,   3,  5,  8,  13,  21,  34….

And it’s architecture upon which much of Creation is built.

It’s staring at us, in our face.

The miracle of Pure Math, combined with Mother Nature.

Even with a lowly dandelion.

..and THAT’s why they amaze me.



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14 Comments on “Getting Mathematical on Weeds.”

  1. Friar Says:

    @Army Wife

    Well, thanks for getting me started on this whole idea…when you mentionned spirals when I posted this photo on FB.

  2. dave1949 Says:

    OF course you realize this proves the case for intelligent design. It is obvious to anyone with an open mind that the dandelion like a lot of other stuff in nature was designed by an exceptional intelligence.
    They were all created by Leonardo Ds Vinci working out the aspects of his code.

  3. Julie Says:

    Deep, this is the best explanation I’ve ever seen. My graphic designer friends have tried explaining it, but my eyes just started their own spiraling! Good job, perfesser.

  4. Dot Says:

    Quite enjoyable and good diagrams! It is fascinating, and makes me wonder whether the Fibonacci series is an innate idea (as in philosophy). We do seem to have an automatic affinity for nature.

    I wrote part of a post about the Fibonacci numbers and sunflowers last year (or so), but most of the post was about something else.

  5. Friar Says:

    I like to think about it as Nature just wanting to take the path of least resistance, and optimizing itself to keep procreating.

    But if people want to attribute this to God, Visnhu or the Flying Spaghetti Monster, then by all means, they can go right ahead. I won’t argue.

    But regardless, I think Ron Howard should make a movie out of it.

    Thanks. I like to explain things.

    Everyone on Facebook gets inspired by all kinds of quotes and advice and words of wisdom. But for me, THIS is the kind of stuff that inspires me. (Shhh…don’t tell anyone) 🙂

    What I like about the Fibnoacci series is that it’s pure arithmetic. Totally devoid of any cultural bias or religious interpretation. There’s something pure about Math that transcends everything else. That’s why I think it’s so cool that it’s tied into the natural world.

  6. Allison Day Says:

    “But for me, THIS is the kind of stuff that inspires me.”

    Me too. ^_^ I LOVE it when you do your Perfessor Friar posts.

  7. Friar Says:


    Oh, THERE you are. I was wondering why you hadn’t shown up yet. 🙂

  8. Eyeteaguy Says:

    Ow, my brain hurts. I think you sprained it.

  9. Friar Says:


    Really? I find this is easy and fun. It’s the computer/IT stuff that makes my brain want to explode.

  10. […] I once wrote a blog post about it here. […]

  11. […] The Dandelion is yet another example of the Fibonacci pattern. […]

  12. […] Getting Mathematical with Weeds […]

  13. […] The Dandelion is yet another example of the Fibonacci pattern. […]

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