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# Problem 226

A Scoop of Blancmange

The blancmange curve is the set of points (x,y) such that 0 ≤ x ≤ 1 and $y=\sum_{n=0}^{\infty} \frac{s(2^n x)}{2^n}$,
where s(x) = the distance from x to the nearest integer.

The area under the blancmange curve is equal to 1/2, shown in pink in the diagram below.

Let C be the circle with centre (1/4,1/2) and radius 1/4, 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

C是以(1/4,1/2)为圆心，半径为1/4的圆，在下图中用黑色标出。