Relates the total Gaussian curvature of a surface to its Euler characteristic, a purely topological quantity. Named for Carl Friedrich Gauss and Pierre Ossian Bonnet, it is a foundational bridge between differential geometry and topology.
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StatementThe Gauss-Bonnet theorem links the total Gaussian curvature of a surface to its topology, expressed through the surface's Euler characteristic. 1 Proof YearGauss developed an earlier version but never published it; Pierre Ossian Bonnet published a special case in 1848. Classification
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1. Gauss-Bonnet Theorem (Wikipedia)
Wikimedia FoundationLead section, opening definition
In differential geometry, the Gauss-Bonnet theorem (or Gauss-Bonnet formula) is a fundamental formula which links the curvature of a surface to its underlying topology.
Lead section, sentence on Gauss and Bonnet's history
The theorem is named after Carl Friedrich Gauss, who developed a version but never published it, and Pierre Ossian Bonnet, who published a special case in 1848.
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