##  [Gauss–Bonnet Theorem](/gauss-bonnet-theorem) 

  ##  [Gauss–Bonnet Theorem](https://puremath.quantumdictionary.io/gauss-bonnet-theorem-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A fundamental result relating the integral of curvature of a compact oriented manifold (or appropriate curvature form in higher dimensions) to a topological invariant of the manifold, the Euler characteristic.