*WILL MEDAL*

if the torsion is identically zero and the curvature is a nonzero constant, then show that the curve is a circle.

I'm suppose to prove that a curve is a circle with the Frenet-Serret formulas but I have no clue how I would prove this.

Question

*WILL MEDAL*

if the torsion is identically zero and the curvature is a nonzero constant, then show that the curve is a circle.

I'm suppose to prove that a curve is a circle with the Frenet-Serret formulas but I have no clue how I would prove this.

irishboy123 · Answer

$\tau = 0$ suggests that the equations simplify: $ \vec T_s = k \vec N, \ \vec N_s = -k \vec T, \  \vec B_s = 0  $

plus: $\vec B = \vec T \times \vec N$ 

i think B is a red herring and that the essence of a circle is that that the tangent and the normal are always perpendicular. 

i would proceed from there.