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Illusion

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?

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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.

Weighty Problem

Stage: 3 Challenge Level: Challenge Level:1

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.

Cabinet on Grid

Presently it is placed (on the X) facing in the direction of the arrows.

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 floor.