Why do this problem
The aim of using this image
is to encourage discussion about the different ways of seeing, and to pose questions that can form the focus of further investigation.
You can find a pdf with the image here
. Look at the image for about a minute and then "hide it". Then share ideas.
Follow up by selecting one or two of the ideas for the group to explore further, for example:
- Recreating the image
- Finding what fraction of the whole the areas is shaded red, blue and white.
Can you continue the pattern inwards? Outwards?
Can you give a convincing argument for the fractions of the whole that you can see?
Consider summing infinite series.
What are the ratios of the lengths of the sides of the triangles?
Can you find the fractions and or recreate the shape by folding? Some learners might like to try the problem Inside Seven Squares