"Paul Ciszek" <email@example.com> wrote in message news:firstname.lastname@example.org... > Picture two Cylinders of radius r that intersect at right angles. > The volume common to both cylinders is a funny looking shape that > is round in cross section in two directions and square in the third. > It will smoothly roll in two orthogonal directions.
> I tried to find the volume of this shape, and I get 16r^3/3. > I would have expected pi to turn up in there somewhere, but > it doesn't.
No, it doessn't. The volume is the sum of rectangular slices. So, no Pi. [ If the cylinders are: x^2 + z^2 = a^2 ; y^2 + z^2 = a^2 , Then the plane: z = c where ( -a .LE. c .LE. a ) is a rectangular cut of the solid of intersection. ]
> Does this shape have a name?
> The shape formed by the intersection of *three* cylinders at right > angles is even cuter. Does it have a name? Has anyone sketched > the shapes produced by cylinders intersecting along other axes, > such as the four diagonals of a cube?