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''''''The '''hairy ball theorem''' of [[algebraic topology]] states that, in layman's terms, "one cannot comb the hair on a ball in a smooth manner".
This fact is immediately convincing to most people, even though they might not recognize the more formal statement of the theorem: there is no nonvanishing [[continuous]] [[tangent vector]] [[vector field|field]] on the sphere. Less briefly, if ''f'' is a [[continuous]] function that assigns a [[vector]] in '''R'''<sup>3</sup> to every point ''p'' on a sphere, and for all ''p'' the vector ''f''(''p'') is a [[tangent]] direction to the sphere at ''p'', then there is at least one ''p'' such that ''f''(''p'') = '''0'''.
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[[Category:Topology]]
[[Category:Algebraic topology]]
[[Category:Theorems]]''''''
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