there is something absurdly exquisite
about this problem.
one elegant volume problem:
this is an icosahedron. suppose it has side length m. if a cylinder of radius 4*m/5 (centered about a vertex) is used to drill through the icosahedron--starting at a chosen vertex, going through the centroid of the solid, and coming out at its opposing vertex--what is the volume that the cylinder has carved out? (in terms of m)
i've not done it yet. but, over about a day's time i'm likely to get bored enough to want to. so, if you were to ask, presumably i'll have a solution.
one elegant volume problem:
this is an icosahedron. suppose it has side length m. if a cylinder of radius 4*m/5 (centered about a vertex) is used to drill through the icosahedron--starting at a chosen vertex, going through the centroid of the solid, and coming out at its opposing vertex--what is the volume that the cylinder has carved out? (in terms of m)
i've not done it yet. but, over about a day's time i'm likely to get bored enough to want to. so, if you were to ask, presumably i'll have a solution.