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 build an imaginary tower of squares inside a right angled
isosceles triangle. The largest square stands on the hypotenuse of
the right angled triangle. Each square has two vertices touching
the other sides of the triangle. Only three squares are drawn in
the diagram but imagine that there are infinitely many getting
smaller and smaller and smaller...
What fraction of the area of the triangle is covered by the
You can do this without a lot of calculation and without any
advanced mathematics. If you wish to extend this project you can
ask: What if the triangle was equilateral? Or what if the tower was
made up of rectangles? Or...