Hairy Ball Theorem

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.

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.