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## 'Up and Across' printed from http://nrich.maths.org/

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...