Editing HairyBallTheorem
You are currently not logged in.
To change this, fill in the following fields:
Username
Password
Who can read this page?
The World
Members
Council
Admin
You have been granted an edit lock on this page
until Fri Mar 29 16:01:13 2024.
Press
to finish editing.
Who can edit this page?
World editing disabled
Members
Council
Admin
If a sphere is covered in hair then the hair cannot be combed to be smooth all over. IMG:hair1.png Somewhere on the sphere must be a point or region to which hair is brushed creating a tuft or from which the hair is brushed away creating a bald patch. For example: IMG:hair2.png IMG:hair3.png IMG:hair4.png More exactly the theorem states that on a sphere there does not exist an everywhere nonzero tangent vector field. A result of this is that somewhere on the surface of the Earth, there is always somewhere a point with zero horizontal wind velocity. It is however possible to comb the hair on a torus to be smooth all over. ---- * http://en.wikipedia.org/wiki/Hairy_ball_theorem * http://mathworld.wolfram.com/HairyBallTheorem.html * http://en.wikipedia.org/wiki/Vector_field