The torsion of a helix Show that the torsion of the helix

Chapter 12, Problem 26E

(choose chapter or problem)

$r(t)=(a \cos t) i\ +\ (a \sin t) j\ +\ b t k, \quad a, b \geq 0$

is $\tau=b /\left(a^{2}\ +\ b^{2}\right)$. What is the largest value $\tau$ can have for a given value of ${a}$? Give reasons for your answer.

Equation Transcription:

$r(t)=(a\ cos\ t)i+(a\ sin\ t)j+btk,\ \ \ a,\ b\geq{}0$

$\tau{}=b/({a}^{2}+{b}^{2})$

$\tau{}$

$a$

Text Transcription:

r(t) = (a cos t)i + (a sin t)j + btk, a, b geq 0

tau = b/(a^2 + b^2)

tau

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