Problem 226
A Scoop of Blancmange

The blancmange curve is the set of points (x,y) such that 0 ≤x≤ 1 and ,
where s(x) = the distance from x to the nearest integer.

The area under the blancmange curve is equal to ½, shown in pink in the diagram below.

blancmange curve

Let C be the circle with centre (¼,&frac12) and radius ¼, shown in black in the diagram.

What area under the blancmange curve is enclosed by C?
Give your answer rounded to eight decimal places in the form 0.abcdefgh

These problems are part of Project Euler and are licensed under CC BY-NC-SA 2.0 UK