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.
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.
The diagram shows a very heavy kitchen cabinet. It cannot be
lifted but it can be pivoted around a corner. That way the cabinet
can be moved in a series of turns about one corner at a time.
Presently it is placed (on the X) facing in the direction of the
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 (and
still placed with its edge on the X). The corners of the cabinet do
not always have to stand on the corners of the square tiles on the