Gaussian Curvature
★★★★☆Undergraduate
📖Definition
Intrinsic curvature of surface. Product of principal curvatures
📐Formulas
K = κ₁ · κ₂
Gauss-Bonnet: ∫∫_S K dA = 2πχ(S)
K = (LN - M²)/(EG - F²)
✏️Examples
예제 1
Plane: K = 0
예제 2
Sphere: K = 1/r²
예제 3
Saddle: K < 0
⚡Applications
Cartography
Surface classification
Topology
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