How Far Does it Move?
Try to approach the problem systematically.
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 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...
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