Doodling in Math Class: Spirals, Fibonacci, and Being a Plant [1 of 3]

Part 2: http://youtu.be/lOIP_Z_-0Hs
Part 3: http://youtu.be/14-NdQwKz9w
Re: Pineapple under the Sea: http://youtu.be/gBxeju8dMho

Say you're me and you're in Math class

and your teacher's talking about-

Well, who knows what your teacher's talking about.

Probably a good time to start doodling

and you're feeling spirally today, so, yeah.

Oh, and because of over-cutting in your school

your Math class is taking place in Greenhouse #3:

Plants!

Anyway, you've decided there are three basic types of spirals.

There's a kind where as you spiral out,

you keep the same distance, or you could start big

and make it tighter and tighter as you go around,

in which case the spiral ends,

or, you could start tight but make it bigger as you go out.

The first kind is good

if you really want to fill up a page with lines

or if you want to draw curled up snakes.

You can start with a wonky shape to spiral around.

But you've noticed that, as you spiral out,

it gets rounder and rounder,

probably something to do with

how the ratio between 2 different numbers approaches 1

as you repeatedly add the same number to both.

But you can bring the wonk back by exaggarating the bumps

and it gets all optical illusiony.

Anyway, you're not sure what the 2nd type of spiral's good for

but it's a good way to draw snuggled up Slug Cats

which are species you've invented

just to keep this spiral from feeling useless.

This 3rd spiral, however, is good for all sorts of things.

You could draw a snail or a Nautilus shell,

an elephant with a curled up trunk,

the horns of a sheep, a fern frond,

a cochlea in an inner ear diagram, an ear itself.

Those other spirals can't help

but be jealous of this clearly superior kind of spiral.

Better draw more Slug Cats.

Here's one way to draw a really perfect spiral:

Start with 1 square, and draw another next to it

that is the same height.

Make the next square fit next to both together.

That is, each side is length 2;

The next square has length 3.

The entire outside shape will always be a rectangle.

Keep spiralling around, adding bigger and bigger squares.

This one has side length 1,2,3,... 12,13, and now 21.

Once you do that, you can add a curve

going through each square, arcing from one corner

to the opposite corner. Resist the urge to zip quickly

across the diagonal if you want a nice, smooth spiral.

Have you ever looked at the spirally pattern on a pinecone

and thought 'hey, sure are spirals on this pinecone'?

I don't know why there're pinecones in your Greenhouse.

Maybe the Greenhouse is in a forest.

Anyway, there're spirals, and there's not just one either.

There are 1,2,3,...8 going this way,

or you could look at the spirals going the other way,

and there are 1,2,3,...12,13.

Look familiar?

8 and 13 are both numbers in the Fibonacci Series.

That's the one where you start by adding 1 and 1 to get 2

and 1 and 2 to get 3, 2 and 3 to get 5,

3+5=8, 5+8=13, and so on.

Some people think that instead of starting with 1+1

you should start with 0 and 1; 0+1=1, 1+1=2, 1+2=3,

and it continues on the same way as starting with 1+1

or I guess you could start with 1+0,

and that would work too

or why not go back one more to -1, and so on.

Anyway, if you're into the Fibonacci Series

you probably have a bunch memorized.

I mean you've got to know 1,1,2,3,5,

finish off the single digits with 8

and oh, 13, how spooky!

And once you're memorizing double digits,

you might at well know 21,34,55,89,

so that whenever someone turns a Fibonacci number,

you can say 'Happy Fibirthday!'

And then, isn't it interesting that 144,233,377?

But 610 breaks that pattern,

so you'd better know that one too...

And oh my goodness, 987 is a neat number!

And, well, you see how these things get out of hand.

Anyway, 'tis the season for decorative, scented pinecones.

and if you're putting glitter glue spirals

on your pinecones, uh, during Math class,

you might notice the number of spirals are 5 and 8,

or 3 and 5, 3 and 5 again, 5 and 8.

This one was 8 and 13

and one Fibonacci pinecone is one thing,

but all of them? What is up with that?

This pinecone has this wumpy, weird part.

Maybe that messes it up. Let's count the top.

5 and 8, now let's check out the bottom: 8 and 13.

If you wanted to draw a mathematically realistic pinecone,

you might start by drawing 5 spirals one way,

and 8 going the other. I'm going to mark out

starting and ending points for my spirals first

as a guide, and then draw the arms,

8 one way, and 5 the other.

Now I can fill in the little pineconey things.

So there's Fibonacci numbers in pinecones,

but are there Fibonacci numbers

in other things that start with 'pine'?

Let's count the spirals on this thing.

1,2,3,... 8, and 1,2,3,... 13.

The leaves are hard to keep track of,

but they're in spirals too, of Fibonacci numbers.

What if we look at these really tight spirals

going almost straight up?

1,2,3,....21! A Fibonacci number.

Can we find a third spiral on this pinecone? Sure!

Go down like this, and...

1,2,3,.... 21!

But that's only a couple examples.

How about this thing I found on the side of the road?

I don't know what it is, it probably starts with 'pine' though.

5 and 8. Let's see how far the conspiracy goes.

What else has spirals in it? This artichoke has 5 and 8.

So does this artichoke-looking flower thing,

and this cactus fruit does too.

Here's an orange cauliflower with 5 and 8,

and a green one with 5 and 8. I mean, 5 and 8.

Oh, it's actually 5 and 8.

Maybe plants just like these numbers though,

doesn't mean it has anything to do with Fibonacci,

does it?

So let's go for some higher numbers.

We're going to need some flowers.

I think this is a flower, it's got 13 and 21.

These daisies are hard to count, but they have 21 and 34.

Now let's bring in the big guns.

1,2,3,4,......34!

And 1,2,3,4,5,........ 55!

I promise this is a random flower

and I didn't pick it out especially to trick you into thinking

that there're Fibonacci numbers in things.

But you should really count for yourself

next time you see something spirally.

There're even Fibonacci numbers

in how the leaves are arranged on this stalk,

or this one,

or the brussel sprouts on this stalk

are a beautiful, delicious 3 and 5.

Fibonacci is even in the arrangement of the petals on this rose,

and sunflowers have shown Fibonacci numbers as high as 144.

It seems pretty cosmic and wondrous,

but the cool thing about the Fibonacci series and spiral

is not that it is this big, complicated,

mystical, magical super-Math thing,

beyond the comprehension of our puny human minds

that shows up mysteriously everywhere.

We'll find that these numbers aren't weird at all.

In fact, it would be weird if they weren't there.

The cool thing about it is

that these incredibly intricate patterns

can result from utterly simple beginnings.