Rotations

The diagram shows a very heavy kitchen cabinet. It cannot be lifted but it can be pivoted around a corner. The task is to move it, without sliding, in a series of turns about the corners so that it is facing the other way round.

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

Can you describe what happens in this film?

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.

Make a footprint pattern using only reflections.

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

Mark a point P inside a closed curve. Is it always possible to find two points that lie on the curve, such that P is the mid point of the line joining these two points?

A design is repeated endlessly along a line - rather like a stream of paper coming off a roll. Make a strip that matches itself after rotation, or after reflection

What is the same and what is different about these tiling patterns and how do they contribute to the floor as a whole?