## rsst123 one year ago *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.

$$\tau = 0$$ 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.