##  [Hairy Ball Theorem](/hairy-ball-theorem) 

  ##  [Hairy Ball Theorem](https://puremath.quantumdictionary.io/hairy-ball-theorem-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A topological theorem stating that any continuous tangent vector field on the 2-sphere S2 must vanish at at least one point; more generally, any continuous tangent vector field on an even-dimensional n-sphere has a zero. In particular there is no nowhere-vanishing continuous tangent vector field on S2.