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
一勺牛奶冻
牛奶冻曲线上的点(x,y)满足0 ≤ x ≤ 1且$y=\sum_{n=0}^{\infty} \frac{s(2^n x)}{2^n}$，
其中s(x)是x与最近的整数之间的距离。
牛奶冻曲线以下的部分，如下图粉色区域所示，其面积为1/2。
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。
牛奶冻曲线以下的部分有多少在圆C中？
将你的答案四舍五入到八位小数，即格式为0.abcdefgh