### 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.

### 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.

### Mystic Rose

Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.

# Notes on a Triangle

##### Stage: 3 Challenge Level:

In the window below, you will see part of the National Film Board of Canada's website.

Click on the arrow in the black and white rectangle to watch "Notes on a Triangle".
You can adjust the volume and pause the film using the buttons underneath the screen (you may have to scroll down a little to see them).

How would you describe what happens in the film?

Can you describe what happens in different sections of the film?
eg 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.