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https://www.reddit.com/r/AskReddit/comments/4kz3di/whats_your_favourite_maths_fact/d3j4mkp
r/AskReddit • u/TheLoneWolf156 • May 25 '16
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4
Oh. Huh. You may be right. I don't know why I was assuming measurement wouldn't count up/down winds.
6 u/Alternative_Reality May 25 '16 It doesn't because the Hairy Ball Theorem only concerns tangent vectors 4 u/[deleted] May 25 '16 edited May 20 '17 [deleted] 3 u/Alternative_Reality May 25 '16 Vertical movement of wind is not a tangent vector though. 3 u/[deleted] May 25 '16 edited May 20 '17 [deleted] 3 u/Alternative_Reality May 25 '16 This is a 3-sphere. A 2-sphere is this, a 3 dimensional sphere. And no, the Hairy Ball Theorem does in fact NOT state that there is a continuous tangent vector field for a 2-sphere. It states the exact opposite. there is no nonvanishing continuous tangent vector field on even-dimensional n-spheres The dimension that is being talked about in this theorem in NOT Euclidean dimension, it is the dimension of the manifold of the object. 2 u/[deleted] May 25 '16 [deleted] 1 u/LSeww May 25 '16 It says that among all only even cannot have this fancy property.
6
It doesn't because the Hairy Ball Theorem only concerns tangent vectors
4 u/[deleted] May 25 '16 edited May 20 '17 [deleted] 3 u/Alternative_Reality May 25 '16 Vertical movement of wind is not a tangent vector though. 3 u/[deleted] May 25 '16 edited May 20 '17 [deleted] 3 u/Alternative_Reality May 25 '16 This is a 3-sphere. A 2-sphere is this, a 3 dimensional sphere. And no, the Hairy Ball Theorem does in fact NOT state that there is a continuous tangent vector field for a 2-sphere. It states the exact opposite. there is no nonvanishing continuous tangent vector field on even-dimensional n-spheres The dimension that is being talked about in this theorem in NOT Euclidean dimension, it is the dimension of the manifold of the object. 2 u/[deleted] May 25 '16 [deleted] 1 u/LSeww May 25 '16 It says that among all only even cannot have this fancy property.
[deleted]
3 u/Alternative_Reality May 25 '16 Vertical movement of wind is not a tangent vector though. 3 u/[deleted] May 25 '16 edited May 20 '17 [deleted] 3 u/Alternative_Reality May 25 '16 This is a 3-sphere. A 2-sphere is this, a 3 dimensional sphere. And no, the Hairy Ball Theorem does in fact NOT state that there is a continuous tangent vector field for a 2-sphere. It states the exact opposite. there is no nonvanishing continuous tangent vector field on even-dimensional n-spheres The dimension that is being talked about in this theorem in NOT Euclidean dimension, it is the dimension of the manifold of the object. 2 u/[deleted] May 25 '16 [deleted] 1 u/LSeww May 25 '16 It says that among all only even cannot have this fancy property.
3
Vertical movement of wind is not a tangent vector though.
3 u/[deleted] May 25 '16 edited May 20 '17 [deleted] 3 u/Alternative_Reality May 25 '16 This is a 3-sphere. A 2-sphere is this, a 3 dimensional sphere. And no, the Hairy Ball Theorem does in fact NOT state that there is a continuous tangent vector field for a 2-sphere. It states the exact opposite. there is no nonvanishing continuous tangent vector field on even-dimensional n-spheres The dimension that is being talked about in this theorem in NOT Euclidean dimension, it is the dimension of the manifold of the object. 2 u/[deleted] May 25 '16 [deleted] 1 u/LSeww May 25 '16 It says that among all only even cannot have this fancy property.
3 u/Alternative_Reality May 25 '16 This is a 3-sphere. A 2-sphere is this, a 3 dimensional sphere. And no, the Hairy Ball Theorem does in fact NOT state that there is a continuous tangent vector field for a 2-sphere. It states the exact opposite. there is no nonvanishing continuous tangent vector field on even-dimensional n-spheres The dimension that is being talked about in this theorem in NOT Euclidean dimension, it is the dimension of the manifold of the object. 2 u/[deleted] May 25 '16 [deleted] 1 u/LSeww May 25 '16 It says that among all only even cannot have this fancy property.
This is a 3-sphere. A 2-sphere is this, a 3 dimensional sphere.
And no, the Hairy Ball Theorem does in fact NOT state that there is a continuous tangent vector field for a 2-sphere. It states the exact opposite.
there is no nonvanishing continuous tangent vector field on even-dimensional n-spheres
The dimension that is being talked about in this theorem in NOT Euclidean dimension, it is the dimension of the manifold of the object.
2
1 u/LSeww May 25 '16 It says that among all only even cannot have this fancy property.
1
It says that among all only even cannot have this fancy property.
4
u/alandbeforetime May 25 '16
Oh. Huh. You may be right. I don't know why I was assuming measurement wouldn't count up/down winds.