Gauss-Bonnet theorem (intro)
General · Mathematics
Study notes
Q: Verify Gauss-Bonnet for sphere radius R. What is ∫K for torus? Sphere: K = 1/R², area 4πR². ∫K dA = (1/R²)(4πR²) = 4π! 2πχ: χ(sphere) = 2: 4π ✓! Torus: χ = 0: ∫K dA = 0 (positive outside, negative inside cancel!)! Triangle: angles sum = π+∫K (spherical excess!)!