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There's still something I want to talk about

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For those students who've never heard of
Fibonacci Numbers, the Wikipedia page

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that I've got on screen now, is a good
place to start. It's actually got

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pictures, so you'll have no trouble
understanding the series. I'm going to

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click on this top picture over here, to expand it,

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so that you see it better in video. The
picture doesn't show the first Fibonacci

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number, because a square
with sides of length 0

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can't be seen, so we're starting with two
squares of length 1,

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side by side. Above that, the next
square has slides of length 2;

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1 plus 1 is 2. To the
left of that we get 3;

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2 plus 1 is 3. Below that is a
square of size 5. Once again, we add

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the previous two values;
3 plus 2 is 5. To the right of

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that we get 8.
Above that is 13, and to the left

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is 21, and so on.
The next square that would

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appear below would have the sides of
length 34;

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21 plus 13 gives 34. We're
moving around in a spiral.

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If I close this picture now and
go back to the Wikipedia article,

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they've included an image of
the spiral you can recreate,

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from Fibonacci numbers.

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Alright, so scrolling down
now, to the nature section,

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down here, there's a picture of a yellow
chamomile flower head.

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I'll click that one over here,
to enlarge it. Apparently,

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the spirals you can draw through the
individual flowers in the flower head,

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are arranged using consecutive Fibonacci
numbers. There is some controversy about

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some of the claims of Fibonacci numbers
appearing in nature. You could probably

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draw all sorts of patterns connecting
the individual flowers, and

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quote unquote, prove just about anything.
I'll admit that my earlier claim, plants

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can understand Fibonacci numbers, was
really just click bait to drag you in,

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but if you thought you weren't good at
maths and are still watching, then it worked.

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I'll close this picture now and scroll
back up to the top of the page.

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Now for the maths stuff. We can see the
first 13 Fibonacci numbers starting at 0,

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and going up to 144. To calculate the
next one,

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we add 144 plus 89. That means the 14th
Fibonacci number,

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which is F 13 because we started at 0,
will be 233. To get the next one, we add

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233 plus 144 giving 377, and that's as much

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maths as you need.
The first two values, F 0 and F 1,

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are 0 and 1. After that, we get each
successive value

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by adding the previous two numbers. So
have a read through this page, and follow

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any links that look interesting,
to learn as much as you want about

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Fibonacci numbers, golden
spirals and so forth.

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I'll stop the video here, and
we'll start writing our code

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in the next video.