Spirals, Fibonacci and being a plant
Doodling in Math: 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
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- 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 overcrowding in your school
- Your math class is taking place in
- Green House #3. Plants.
- Anyway, you've decided there's three basic types of spirals.
- There's the kind where as you spiral out, you keep the same distance
- Or could start big but make it tighter and tighter as you go around in which case the spiral ends.
- Or you could start tight and but make the spiral bigger as you go out.
- The first kind is good if you really want to fill up the page with lines.
- Or if you wanna draw curled up snakes.
- You can start with a wonky shape to spiral around,
- but you 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's 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, 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 one 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 two
- The next square is length three.
- The entire outside shape will always be a rectangle.
- Keep spiraling around, adding bigger and bigger squares.
- This one has side length... (1, 2, 3, 4, 5, 6, 7, 8, 9, 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 the spiraly pattern on a pinecone and thought:
- Hey, sure are spirals on this pinecone?
- I don't know why there's pinecones in your greenhouse, maybe your greenhouse is in a forest.
- Anyway, there's spirals, and there's not just one either.
- There's... (1, 2, 3, 4, 5, 6, 7) 8 going this way.
- Or you could look at the spirals going the other way and there's
- (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12) 13. Look familiar?
- Eight and thirteen 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 thirteen, and so on.
- Some people think that instead of starting with one plus one, you should start with zero and one.
- Zero plus one is is one, one plus one is two, two plus one is three,
- and it continues on the same way as starting with one and one.
- Or I guess you could start with one plus zero
- 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 gotta know one, one, two, three, five,
- finish off the single digits with eight,
- and ooh thirteen, how spooky!
- And once you're memorizing double digits
- you might as well know twenty-one, thirty-four, fifty-five, eighty-nine;
- So whenever someone turns a Fibonacci number
- you can say "Happy Fib-birthday!"
- And then isn't it interesting that one-fourty-four, two-thirty-three,
- three-seventy-seven, but six-ten breaks that pattern
- so you better know that one too, and
- oh my goodness, nine-eight-seven 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 that the number of spirals
- are five and eight; or three and five;
- three and five again; five and eight;
- this one was eight and thirteen.
- 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--
- five and eight. Now let's check out the bottom--
- eight and thirteen.
- If you wanted to draw a mathematically
- realistic pinecone, you might
- start by drawing five spirals going one way
- and eight going the other.
- I'm gonna 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 pinecone-y 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.
- (One, two, three, four, five, six, seven,) Eight, and
- (one, two, three, four, five, six, seven,
- eight, nine, ten, eleven, twelve,)
- Thirteen.
- 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?
- (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20) 21.
- A Fibonacci number.
- Can we fina the third spiral on this pinecone?
- Sure, go down like this and...
- (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20) 21.
- But that's only a couple of examples.
- How about this thing I found by 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 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 gonna 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.
- (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20...
- ...21,22,23,24,25,26,27,28,29,30,31,32,33) 34.
- And (1,2,3,4,5,6,7,8,9,10,11... *skips a few* ...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 3 and 5.
- Fibonacci is even in the arrangement of the
- petals on this rose and some flowers have
- shown Fibonacci numbers as high as 144.
- It's 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.
Be specific, and indicate a time in the video:
At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?
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