## A Scoop of Blancmange

### Problem 226

Published on Friday, 2nd January 2009, 09:00 pm; Solved by 1228; Difficulty rating: 65%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.

Let `C` be the circle with centre (¼,½) 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*