Rotations

A security camera, taking pictures each half a second, films a cyclist going by. In the film, the cyclist appears to go forward while the wheels appear to go backwards. Why?

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.

What is the volume of the solid formed by rotating this right angled triangle about the hypotenuse?

Points off a rolling wheel make traces. What makes those traces have symmetry?

I noticed this about streamers that have rotation symmetry : if there was one centre of rotation there always seems to be a second centre that also worked. Can you find a design that has only one centre of rotation ? Or if you thought that was impossible, could you say why ?

Can you see which tile is the odd one out in this design? Using the basic tile, can you make a repeating pattern to decorate our wall?

Watch this "Notes on a Triangle" film. Can you recreate parts of the film using cut-out triangles?

How can these shapes be cut in half to make two shapes the same shape and size? Can you find more than one way to do it?

What happens to these capital letters when they are rotated through one half turn, or flipped sideways and from top to bottom?