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Elephants, Camels and...apollonian gaskets?

Have you ever wished for a game that you can do anytime during math? hm... why not try apollonian gaskets? as we will take up the challenge of infinates and animals.
by

Natalie Chan

on 13 February 2011

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Transcript of Elephants, Camels and...apollonian gaskets?

Elephants, Camels
and...
Apollonian gaskets? You know what an elephant is, as well as a camel! But what is an Apollonian gasket you may ask? Simple. Think of it as a math game. Don't worry, no calculators needed!
*horrible way to get you to laugh*
*now you laugh.* For example! Create a circle or, any shape to your liking! Now, try to draw the biggest circle that you can fit in the shape.
Note: doesn't have to be perfect! Just let
your hand guide you. If its a circle, you might want to draw 2-4 circles that are the same size, but smaller than the original, to be able to fit into the circle. Now, try drawing the biggest circle in the space left, the gaps between the big circle(s), and continue to do so with the remaining space. Look's interesting, no? Congratulations, you have made a pattern or now known, an apollonian gasket! This leads you to the infinite. But wait, aren't we talking about apollonian gaskets?
Yes, we are! Infinites are a topic that will be taught in Math class in high school but is necessary in an apollonian gasket. But, heres a quick doodle game about infinites and apollonian gaskets. An apollonian gasket is a shape made up of circles and smaller circles which will then create a pattern. An apollonian gasket involves the infinite. Where one shape will have circles swirling inside the shape! That still doesn't clear up the fact of the infinite, does it? Well, the infinite is involved because once one circle is drawn, a smaller one will too! and so on and so on until it can't be visable with the eye. It's quite easy, isn't it! Try to decorate it afterwards! it can be smiles in a shape, roses blooming or even a monster eating one another! Possibilites are endless. So what does this have to do with Elephants and Camels? Another simple idea. Try watching this video: Couldn't follow? Don't worry, its understandable considering she spoke so fast! So, back to the Elephants and Camels if you couldn't follow Say, for some strange reason, you wanted to draw an animal linked to another and another and so on. BUT! Each animal gradually shrinks until it can't be seen. this is where the infinite takes place! . The problem is, you don't know the percentage of how small each animal will be drawn! This could be figured through effort of time and math ...Or the easy way. Remember how each circle drawn in a shape continuously shrinks in a certain pattern? Now imagine that but instead, the shape will be a triangle Now try doing the apollonian gasket with the circles going straight to the point of the triangle. This will give an outline to how big each drawing will be!

Simple as that and as promised, no calculators. Another thing that wasn't touched upon was why i chose to talk about the Apollonian Gasket! The reason why I chose this topic was because i stumbled onto the video that was shown moments ago which got me interested. And because I loved to draw, it gave me an inspiration to draw this: And the circles will represent the animal! The drawing is of a peacock, looking high and mighty as always with it's head cocked away, with a big tail that was inspired by the apollonian gasket. One more thing, the apollonian gasket doesnt have to be just tied down to circles, you can draw triangles, rectangles, hearts and even little animals covering all over! And one
more
thing! If you think your up to the challenge... Try replacing circles with anything! This has been brought to you by ZEBRAS! Nature's wonder.
Is it white stripes on black,
or
black stripes on white? Pronounciation? Apollonian Gasket
(Ap-o-lone-e-an Gas-ket) Definition?
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