Postby **phlip** » Mon Apr 06, 2009 7:43 am UTC

I got the same result as doogly (except I get a radius of (sqrt(n)-1)/2, not (sqrt(n)-1)/4, but the result is the same). [edit] Actually, I misread before the picture was added, that the corner spheres were centred on the points of the cube, not inscribed like that. But having them inscribed in a cube of side length 1 is the same as having them centred on the corners of a cube of side length 1/2, so (sqrt(n)-1)/4 is correct. [/edit]

Simplified to only the cases where the dimension is even, since the volume-of-a-hypersphere formula is simpler (and if there's a limit for all n, then there will be a limit for even n), and plugging numbers into Python, I get it seeming to increase without bound for the numbers I plugged in.

Of interest: in four [edit] Again, misread: actually, nine [/edit] dimensions, the inner sphere is tangent to the 16 [edit] 512 [/edit] corner spheres, and tangent to the cube. For higher dimensions, the sphere will protrude from the cube.

Code: Select all

`enum ಠ_ಠ {°□°╰=1, °Д°╰, ಠ益ಠ╰};`

void ┻━┻︵╰(ಠ_ಠ ⚠) {exit((int)⚠);}

[he/him/his]