[mbriklly] Circle in square

Draw a circle inside a square so that the area inside the circle is the same as the area outside the circle but inside the square.  For a unit square, the radius is
1/Sqrt(2*pi) = 0.3989422804014327

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For sphere inside unit cube, the radius is 0.492373. In 4 dimensions and above, the sphere won't fit, or you need to do messy calculations of a truncated hypersphere.