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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... 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 the kind where as you spiral out, you keep the same distance, or you could start big and make it 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. Probably something to do with how the ratio between two different numbers approaches 1 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 type of spiral's good for but it's a good way to draw snuggled up Slug Cats which are a species you've invented just to keep this 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 but I 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 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 your Greenhouse is in a forest. Anyway, there're spirals, and there's not just one, there're 8 going this way, or you could look at the spirals going the other way, and there're 13. Look familiar? 8 and 13 are 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 plus 5 is 8, 5 plus 8 is 13, and so on. Some people think that instead of starting with 1 plus 1 you should start with 0 and 1; 0 plus 1 is 1, 1 plus 1 is 2, 1 plus 2 is 3 and it continues on the same way as starting with 1 and 1. Or I guess you could start with 1 plus 0, and that would work too or go back one more to -1, and so on.

Anyway, if you're into the Fibonacci Series you probably have a bunch memorised, 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 memorising 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!

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 and make it 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. Probably something to do with how the ratio between two different numbers approaches 1 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 type of spiral's good for but it's a good way to draw snuggled up Slug Cats which are a species you've invented just to keep this 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 but I 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 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 your Greenhouse is in a forest. Anyway, there're spirals, and there's not just one, there're 8 going this way, or you could look at the spirals going the other way, and there're 13. Look familiar? 8 and 13 are 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 plus 5 is 8, 5 plus 8 is 13, and so on. Some people think that instead of starting with 1 plus 1 you should start with 0 and 1; 0 plus 1 is 1, 1 plus 1 is 2, 1 plus 2 is 3 and it continues on the same way as starting with 1 and 1. Or I guess you could start with 1 plus 0, and that would work too or go back one more to -1, and so on.

Anyway, if you're into the Fibonacci Series you probably have a bunch memorised, 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 memorising 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!

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