Curvy areas

Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Curvy Areas printable sheet 

Curvy Areas downloadable slides

 

Take a look at the image below:

Image
Curvy areas

 

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.

Image
Curvy areas
Image
Curvy areas


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.