Obtain and in Prob. 52 from (22*) and (23***) and the original representation in Prob. 54 with parameter t. Data from Prob. 52

Obtain κ and τ in Prob. 52 from (22*) and (23***) and the original representation in Prob. 54 with parameter t.

Data from Prob. 52

Show that the helix [α cos t, α sin t, ct] can be represented by [α cos (s/K), α sin (s/K), cs/K], where K = √α² + c² and s is the arc length. Show that it has constant curvature k = α/K² and torsion τ = c/K². 

Data from Prob. 54

Show that