Hairy Ball Theorem
المؤلف:
Steinhaus, H
المصدر:
Mathematical Snapshots, 3rd ed. New York: Dover
الجزء والصفحة:
...
1-6-2021
2175
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.
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