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.

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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:

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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?

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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.

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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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Tags: dandelion, Fibonacci Sequence, flowers, Golden Ratio

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