Some of you may be familiar with the Wallis sieve, the geometric realization of the Wallis product to get pi/4
But did you know that that's not just a random multiple of pi, but actually meaningfully the area of the fractal's bounding box's inscribed circle?
And did your know that the same holds for a generalized sieve in N dimensions, giving the volume of the N-ball?
I've never seen a general proof, does /sci/ know something about this?