There does not exist an everywhere nonzero tangent vector field on the 2-sphere 
. This implies that somewhere on the
surface of the Earth, there is a point with zero horizontal wind velocity. The theorem
can be generalized to the statement that the 
-sphere 
has a nonzero tangent vector field iff 
is odd.
Hairy Ball Theorem
See also
Fixed Point TheoremExplore with Wolfram|Alpha
References
Steinhaus, H. Mathematical Snapshots, 3rd ed. New York: Dover, pp. 279-281, 1999.Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. Middlesex, England: Penguin Books, p. 90, 1991.Referenced on Wolfram|Alpha
Hairy Ball TheoremCite this as:
Weisstein, Eric W. "Hairy Ball Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HairyBallTheorem.html