Curvy Areas

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 smaller images created in a similar way.


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

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.