Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?
Investigate how this pattern of squares continues. You could
measure lengths, areas and angles.
Can you work out the area of the inner square and give an
explanation of how you did it?
We received correct solutions (that the areas were all the same) from:
Well done all of you.
I particularly liked Michael's solution because he generalised the result and I have used this as the basis of what follows. Although it was not intended to be a trick question Michael!