hi,
for most of you this might be a simple question:
Is it possible to embed the flat torus in Euclidean space?
If we, for example, take a rectangle and identify the left and the right sides we get a cylinder shell, that can be embedded easily in R^3. If we construct the...
Hi, I need to find the volume of the solid that lies above the cone with equation (in spherical coordinates) \phi = \frac{\Pi}{3} and inside the torus with equation \rho = 4\sin\phi . I thought that the bounds are: 0\leq\rho\leq4\sin\phi, \frac{\Pi}{3}\leq\phi\leq\frac{\Pi}{2}, and...
I'm asked to consider regular networks on a torus. I'm given that V - E + F = 0. I need to show it is impossible to have a regular network on a torus where the faces are pentagons; I don't understand that at all. Surely it is easy to have pentagons as faces… All you would need to is draw a...
Hi!
This may not be the right place for it but I have a question about the torus.
In the centre point, the exact middle of the hole in the torus if a let's say, a perfect sphere was placed there, would it simply stay in the one place if everything was stationary?
Also could you walk all...
Hi,
A small but exceptionally annoying algebraic topology question:
I'm trying to find the Hodge numbers (from the Hodge-de Rham cohomology) for a 2n-dimensional torus (that is, n complex dimensions).
Anyone have any ideas? It's a rather technical question, but I don't really want to...
There is a developing theory that the Universe may be shaped like a three-torus, the mathematical equivalent of a rubber cube that's bent so that all opposing sides are connected. This would mean that the Universe is finite, but does not have the problematic edge that's included in most...