Curvy Areas printable sheet 
Curvy Areas downloadable slides
 

Take a look at the image below:

Can you see how the image was created?
Try to recreate it using a ruler and compasses.


Here are two images created in a similar way.


Can you work out the proportion of the 3-colour, 4-colour and 5-colour circles which is shaded red?
Can you make any generalisations?
Can you prove your ideas?


Extension
What about the proportion which is shaded orange? Yellow? ... 
Can you make any generalisations?
Can you prove your ideas? 

Click here for a poster of this problem.