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Rolling Triangle

The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.

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Turning Triangles

A triangle ABC resting on a horizontal line is "rolled" along the line. Describe the paths of each of the vertices and the relationships between them and the original triangle.

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An animation that helps you understand the game of Nim.

Notes on a Triangle

Age 11 to 14 Challenge Level:

For this task, you will need to watch the short film Notes on a Triangle, on the National Film Board of Canada's website.

How would you describe what happens in the film?

Can you describe what happens in different sections of the film?
For example, 1 - 34 seconds and 35 - 45 seconds may provide two natural sections to focus on at the beginning.

What mathematical properties remain constant throughout your chosen clip?

Could a section of the dance be performed by a different shape?
Imagine replacing the triangle with a kite, or a rhombus, or an arrowhead, or ...

How would you cut up your new shape to produce congruent pieces?
Can your new shape(s) still achieve the same movements and symmetries?

If you produce a wall display do send us some photos.

Here is a sheet of equilateral triangles for you to print off and cut out (using coloured paper might be a good idea) if you want to recreate some of the images in the film.