First fundamental form
General · Mathematics
Study notes
Q: Compute E,F,G for plane X(u,v) = (u,v,0) and sphere radius R. Plane: X_u = (1,0,0), X_v = (0,1,0). E = 1, F = 0, G = 1: I = du²+dv² (flat!). Sphere R: X(θ,φ): X_θ = R(-sinφsinθ,sinφcosθ,0), X_φ = R(cosφcosθ,...). E = R²sin²φ, F = 0, G = R²: I = R²(sin²φdθ²+dφ²). (Intrinsic geometry!)