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• Voiceover:Say [unintelligible], you're in math class

• Probably a good time to start doodling.

• And you're feeling spirally today, so yeah.

• Oh, and because of overcrowding in your school,

• your math class is taking place in

• greenhouse number three.

• Plants.

• Anyway.

• You've decided there are three basic

• types of spirals.

• There's the kind where, as you spiral out,

• you keep the same distance.

• Or you could start big but make it tighter

• and tighter as you go around, in which case

• the spiral ends.

• Or you could start tight but make the spiral

• 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.

• but you've noticed that, as you spiral out,

• it gets rounder and rounder.

• Probably something to do with how the ratio

• between two different numbers approaches one

• as you repeatedly add the same number to both.

• But you can bring the wonk back by

• exaggerating the bumps and it gets all

• optical illusiony.

• Anyway, you're not sure what the second

• kind of spiral is good for, but I guess it's

• a good way to draw snuggled up slug cats,

• which are a species you've invented just

• to keep this kind of spiral from feeling useless.

• This third spiral, however, is good for

• all sorts of things.

• You could draw a snail or a nautilus shell.

• And 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.

• But I draw more slug cats.

• Here's one way to draw a really perfect spiral.

• next to it that is the same height.

• Make the next square fit next to both together,

• that is each side is length two.

• The next square has length three.

• The entire outside shape will always

• be a rectangle.

• Keep spiraling around, adding bigger

• and bigger squares.

• This one has side length one, two, three,

• four, five, six, seven, eight, nine,

• 10, 11, 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 pine cone and thought, "Hey, sure are

• "spirals on this pine cone?"

• I don't know why there's pine cones

• Maybe the greenhouse is in a forest.

• Anyway, there's spirals and there's not

• just one either.

• There's one, two, three, four, five, six,

• seven, eight going this way.

• Or you could look at the spirals going

• the other way and there's one, two, three,

• four, five, six, seven, eight, nine, 10, 11, 12, 13.

• Look familiar?

• Eight and 13 are both numbers in the

• Fibonacci series.

• That's the one where you start by adding

• one and one to get two, then one and two

• to get three, two and three to get five.

• Three plus five is eight, five plus eight

• is 13, and so on.

• Some people think that instead of starting

• zero and one.

• Zero plus one is one, one plus one is two,

• one plus two and three, and it continues

• on the same way as starting with one and one.

• and that would work too.

• Or why not go back one more to negative one

• and so on?

• Anyway, if you're into the Fibonacci series,

• you probably have a bunch memorized.

• I mean, you've got to know one, one, two,

• three, five.

• Finish off the single digits with eight

• and, ooh with 13, how spooky.

• And once you're memorizing double digits,

• you might as well know 21, 34, 55, 89 so that

• whenever someone turns a Fibonacci number

• you can say, "Happy Fib Birthday."

• 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 pine cones and if you're putting

• glitter glue spirals on your pine cones

• during math class, you might notice that

• the number of spirals are five and eight

• or three and five or three and five again.

• Five and eight.

• This one was eight and thirteen and one

• Fibonacci pine cone is one thing, but all of them?

• What is up with that?

• This pine cone has this wumpy weird part.

• Maybe that messes it up.

• Let's count the top.

• Five and eight.

• Now let's check out the bottom.

• Eight and 13.

• If you wanted to draw a mathematically

• realistic pine cone, you might start

• by drawing five spirals one way and eight

• 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.

• Eight one way and five the other.

• Now I can fill in the little pine coney things.

• So there's Fibonacci numbers in pine cones

• but are there Fibonacci numbers in other things

• Let's count the spirals on this thing.

• One, two, three, four, five, six, seven, eight.

• And one, two, three, four, five, six, seven,

• eight, nine, 10, 11, 12, 13.

• The leaves are hard to keep track of,

• but they're in spirals too.

• Of Fibonacci numbers.

• What if we looked at these really tight spirals

• going almost straight up?

• One, two, three, four, five, six, seven,

• eight, nine, 10, 11, 12, 13, 14, 15, 16, 17,

• 18, 19, 20, 21.

• A Fibonacci number.

• Can we find a third spiral on this pine cone?

• Sure, go down like this.

• And one, two, three, four, five, six, seven,

• eight, nine, 10, 11, 12, 13 (muttering) 19, 20, 21.

• But that's only a couple examples.

• on the side of the road?

• I don't know what it is.

• It probably starts with pine, though.

• Five and eight.

• Let's see how far the conspiracy goes.

• What else has spirals in it?

• This artichoke has five and eight.

• So does this artichoke looking flower thing.

• And this cactus fruit does too.

• Here's an orange cauliflower with five and eight

• and a green one with five and eight.

• I mean, five and eight.

• Oh, it's actually five and eight.

• 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.

• One, two, three, four, five, six, seven,

• eight, nine, 10, 11, 12, 13, 14, 15, 16, 17,

• 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30,

• 31, 32, 33, 34.

• And one, two, three, four, five, six, seven,

• eight, nine, 10, 11, (muttering) 17, 24,

• (muttering) 42, 53, 54, 55.

• I promise, this is a random flower and I didn't

• pick it out specially to trick you into thinking

• there's Fibonacci numbers in things, but you should

• really count for yourself next time you see

• something spirally.

• There's even Fibonacci numbers in how

• the leaves are arranged on this stalk,

• or this one, or the Brussels sprouts on this stalk

• are a beautiful delicious three and five.

• 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's 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.

Voiceover:Say [unintelligible], you're in math class

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