Fiery tsunami on a sunny day
I was playing around with some ideas for a nice geometry puzzle involving circles on my iPad when my daughter saw it and said it looked like fire. I then added some background elements like the sun, the cloud, the sky, and the land, and now it looks like a tsunami of fire on a sunny day!
Anyway, here’s the question. What fraction of the image is covered in fire? And more importantly, can you find it with as little calculation as possible?
Clarifications:
- All curves in the fire are circular arcs of 90º.
- The angle between any two curves, wherever they meet, is a multiple of 45º.
- The point where the biggest red and orange parts meet is the centre of the big circle.
- The fire extends all the way to the horizon.