Wikipedia:Reference desk/Archives/Mathematics/2013 March 23
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March 23
[edit]Nonconvex polyhedra
[edit]What's the smallest number of faces a concave polyhedron can have? A self-intersecting one? What if the faces themselves must be convex? Double sharp (talk) 14:37, 23 March 2013 (UTC)
- I suppose that the empty set qualifies as a polyhedron: It is a subset of three dimensional space, all edges are straight and all faces are plane. So the answer is zero. Bo Jacoby (talk) 15:30, 23 March 2013 (UTC).
- LOL. Excluding this, then? Double sharp (talk) 16:29, 23 March 2013 (UTC)
- Possibly six: a tetrahedron minus a lower tetrahedron on the same base. And I can't see for now how that could be less than six. --CiaPan (talk) 23:11, 23 March 2013 (UTC)
- You can do it with five faces if they don't have to be convex. Just think tertrahedron with one side chopped away a bit so it forms two faces. Dmcq (talk) 23:19, 23 March 2013 (UTC)
- That would still be six faces, wouldn't it? The tetrahedron has four faces, and then you're forming two new faces from one of its edges. Maybe I'm not correctly visualizing what you're describing. —Bkell (talk) 23:35, 23 March 2013 (UTC)
- No two faces from one face. Altogether you get six points, nine lines and five faces. Dmcq (talk) 01:33, 24 March 2013 (UTC)
- Oh, I see it now. It's a pyramid with a base that is a concave quadrilateral. That has five faces, five vertices, and eight edges, right? —Bkell (talk) 05:30, 24 March 2013 (UTC)
- Yes that shape is right. I had a line across the face but if it ends at one of the vertices yes you can cut it down to five vertices and eight edges, don't know why I didn't think of that, thanks. Dmcq (talk) 11:48, 24 March 2013 (UTC)
- Oh, I see it now. It's a pyramid with a base that is a concave quadrilateral. That has five faces, five vertices, and eight edges, right? —Bkell (talk) 05:30, 24 March 2013 (UTC)
- No two faces from one face. Altogether you get six points, nine lines and five faces. Dmcq (talk) 01:33, 24 March 2013 (UTC)
- That's right, Dmcq, I must have limited myself somehow to use convex faces only. --CiaPan (talk) 19:03, 24 March 2013 (UTC)
- That would still be six faces, wouldn't it? The tetrahedron has four faces, and then you're forming two new faces from one of its edges. Maybe I'm not correctly visualizing what you're describing. —Bkell (talk) 23:35, 23 March 2013 (UTC)
- You can do it with five faces if they don't have to be convex. Just think tertrahedron with one side chopped away a bit so it forms two faces. Dmcq (talk) 23:19, 23 March 2013 (UTC)
mechanics
[edit]tell me the method to find the moment of inertia...write in detail — Preceding unsigned comment added by 204.14.79.224 (talk) 19:16, 23 March 2013 (UTC)
- See moment of inertia and come back to us if you have a more specific question. Rojomoke (talk) 19:52, 23 March 2013 (UTC)