Regular surfaces
General · Mathematics
Study notes
Q: Parametrize the unit sphere. Find the tangent plane at (0,0,1). X(θ,φ) = (sinφcosθ, sinφsinθ, cosφ). X_θ = (-sinφsinθ, sinφcosθ, 0). X_φ = (cosφcosθ, cosφsinθ, -sinφ). X_θ×X_φ: at north pole φ = 0: X_θ = 0 (singular - poles!). Use different patch or: normal at (0,0,1) is (0,0,1). Tangent plane: z = 1! (Regular: need X_u×X_v ≠ 0!)