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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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Walk and Ride

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Speeding Up, Slowing Down

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Try to approach the problem systematically, keeping one variable fixed and just altering the other one.

As you go along try to understand why the graph takes the shape that it does:
  • by relating it to the rolling polygon and the journey of the red dot
  • by trying to predict what will happen before you set the polygon rolling
Could the dot have been on the centre of a polygon?
Try for each of the polygons.

Could the dot have been on the centre of the base of a polygon?
Try for each of the polygons.

Could the dot have been on the centre of one of the sloping sides of a polygon?
Try for each of the polygons.

Could the dot have been on the centre of a side opposite the base of a polygon?
Try for each of the polygons.

Could the dot have been on a vertex opposite the base of a polygon?
Try for each of the polygons.

Could the dot have been on a vertex on the base of a polygon?
Try for each of the polygons...

Alternatively...
  • try all possible positions of the dot in a triangle,
  • and then in a square,
  • and then in a pentagon,
  • and then in a hexagon...