Gauss–Bonnet theorem
Theorem in differential geometry / From Wikipedia, the free encyclopedia
Dear Wikiwand AI, let's keep it short by simply answering these key questions:
Can you list the top facts and stats about Gauss–Bonnet theorem?
Summarize this article for a 10 year old
SHOW ALL QUESTIONS
"Gauss–Bonnet" redirects here. Not to be confused with Gauss–Bonnet gravity.
In the mathematical field of 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.
This article needs additional citations for verification. (October 2020) |
In the simplest application, the case of a triangle on a plane, the sum of its angles is 180 degrees.[1] The Gauss–Bonnet theorem extends this to more complicated shapes and curved surfaces, connecting the local and global geometries.
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.[not verified in body]