Obtain and in Prob. 52 from (22*) and (23***) and the original representation in Prob.
Question:
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
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From Prob 52 we know that the helix cos t sin t ct can be represented by cos sK sin sK c...View the full answer
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