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

🔗Related Documents

Prerequisites

#가우스#Gaussian#곡률#curvature