A grey square has a white circle inscribed and a grey square inscribed in the circle.
What fraction of the diagram is white?
Area of outside square = 2r 2r = 4r2
Area of inside square = ½ 4r2 = 2r2
Area of circle = πr2
Area white = πr2 2r2 = r2(π 2)
Hence, fraction of the diagram white = r2(π 2)/4r2 = (π 2)/4 0.285
If another white circle was inscribed in the inside square, what fraction would be white now?
What would happen if white circles and grey squares were recursively inscribed? Would the white area tend towards a limit?