5 ms·
In fact, it does -- to demonstrate, assume otherwise and use the definition of continuity.
by pndmnm 13y ago
In fact, it does -- to demonstrate, assume otherwise and use the definition of continuity.
- rtkwe 13y agosigh To quote because topology is a pain: > "there is no nonvanishing continuous tangent vector field on even dimensional n-spheres. For the ordinary sphere, or 2‑sphere, if f is a continuous function that assigns a vector in R3 to every point p on a sphere such that f(p) is always tangent to the sphere at p, then there is at least one p such that f(p) = 0" Which means they can all blow in a continuous path except for at least one point, so the wind at every point but 2 could be blowing east on a sphere. http://en.wikipedia.org/wiki/Hairy_ball_theorem http://en.wikipedia.org/wiki/Hairy_ball_theorem
- lutorm 13y agoYes, but the velocity must go to zero as you approach the poles. I took the OP to mean "with the same velocity", not "in closed loops". Obviously wind must blow in closed loops, since there are no sources or sinks of air.
- dogecoinbase 13y agoSo to you, "pointing in the same direction" includes "pointing in exact opposite directions within an epsilon-ball for any epsilon"?
- xyzzyz 13y agoThere's a whole continuum between "pointing in the same direction" and "pointing in exactly opposite directions".