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Mathematics
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Geometry
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Gauss-Bonnet Theorem
Gauss-Bonnet Theorem
A deep link between geometry and topology.
📜
The statement of the theorem
Connects the geometry of a surface (its curvature) to its topology (its Euler characteristic).\n
∫
M
K
d
A
=
2
π
χ
(
M
)
\int_M K \, dA = 2\pi \chi(M)
∫
M
K
d
A
=
2
π
χ
(
M
)
Source: Wikipedia