Archive for the ‘Tessellations’ Category

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Thinking, Thinking, Thinking Maths

May 29, 2012

Now, my Sweeties, I want you to understand something important about the way people, who use maths, think.

It is vital that architects can walk around inside an imaginary building in their heads, that engineers can see in their imagination where the support columns need to be placed in a building/bridge, that chemists can visualise 3D mirror images of molecules, that fashion designers can see the axis of symmetry and also invert an item of clothing inside out (because that is how clothes are sewn), that designers can rotate objects in their imagination (not just to look pretty, but to make sure the object can stand up) and it is important that computer programmers can see patterns to write their repeating algorithms (More later).

The maths involved here includes:

Symmetry

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2D patterns

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2D & 3D mirror images

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3D Rotations

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Algorithms

You will find these fab world maps @ BLDG BLOG, which uses an algorithm to map the 3D world into different 2D shapes, which can then be reconstructed into 3D objects. Wow!

Sometimes mathspiggies, teachers forget how important these visualising exercises can be in the development of maths thinking skills.

So my little Sweeties, we’re going to use some of these maths skills to build up your maths brain.

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1. Rotating Tessellation

A tessellation is a repeating pattern with no gaps like floor tiles.

This Leaf Tessellation came from almostunschoolers blog

Look at the pattern. It involves equilateral triangles repeated.


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Oops! Not exactly perfect, but Mathspig was using paper and scissors!

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We aren’t going to write a computer program, but rather think what we might want the program to do. The Rotation Tessellation algorithm would go something like this. Take triangle shape, rotate around fixed point A until area tiled, stop. Take new fixed point, rotate new shape around this point until all area tiled, repeat, repeat, repeat.

2. Flip Tessellations

This time we will use mirror images, which we create by flipping an image.

As the Eurovision Song contest has just finsihed we’ll use an image of the Twin Brothers Jedward to create our flip tessellation. You can use any image to create a flip tessellation, even your own head!!!!!!!!! First I took one brother.

Then I flipped him horizontally.

Then I flipped him vertically

and then I just kept going.. unfortunately, I had to print and scan to get the wallpaper effect.

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We could create an algorithm, which tells the computer to do this: Take Jedward 1, flip horizontal, flip last pic vertical, flip last pic horizontal, copy new pic, flip horizontal, flip vertical, flip horizontal, repeat, repeat…………….

In fact, Mathspig had an JEDWARD algorithm in her head, copy, paste, copy, paste, copy, paste….. Arghhhhhhh! ….couldn’t stop…..

But you end up with a lovely set of JEDWARD floor tiles, or curtain fabric or maybe shirt material!!!!!! Nice! It depends on your taste, really.

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