TOPICS
Search

Hairy Ball Theorem


There does not exist an everywhere nonzero tangent vector field on the 2-sphere S^2. 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 n-sphere S^n has a nonzero tangent vector field iff n is odd.


See also

Fixed Point Theorem

Explore 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 Theorem

Cite this as:

Weisstein, Eric W. "Hairy Ball Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HairyBallTheorem.html

Subject classifications