Frenet-Serret formulae
General · Mathematics
Study notes
Q: For unit circle r(s) = (cos s, sin s, 0), find T, N, B and verify Frenet-Serret. T = r' = (-sin s, cos s, 0). T' = (-cos s,-sin s,0): κ = 1: N = (-cos s,-sin s,0). B = T×N = (0,0,1) (check: (-sin)(-sin)-(cos)(-cos)... = (0,0,sin²+cos²) = (0,0,1) ✓). T' = κN = 1·N ✓! N' = -T+0·B = -T ✓ (τ = 0)! B' = 0 ✓!