Gauss–Bonnet theorem

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What Wikipedia says

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.

Excerpt from the Wikipedia article “Gauss–Bonnet theorem”, under the CC BY-SA 4.0 license. Read the article on Wikipedia

Image: Wladik Derevianko, Public domain, via Wikimedia Commons.