Generalising with Areas of Circles

Screen Shot 2016-03-24 at 21.03.04

So, at #MathsMeetGlyn last weekend Don Steward briefly put this picture up on the screen but then decided to talk about something else as time was pressing.

That’s a bit like a “Wet Paint” sign.  You have to touch it just to see if it really is wet…

So I had a little play with these. I couldn’t find anything about it on his blog but of course there is lots of other lovely stuff there.

A few different questions you could pose here:

  • What is the ratio of red area to blue area?
  • What is the red area as a fraction of the blue area?
  • What is the red area as a fraction of the whole circle?
  • What is the blue area as a fraction of the whole circle?

And then of course, can we generalise?  What about when there are n small circles.  What happens as n gets bigger? Why? Can we find a general expression for the area?

Have a go.  It actually turns out to be quite simple but depending on which question you start with, you can get into a lot of practice with ratio and dividing fractions.

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