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  • 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.

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  1. IrishBoy123
    • one year ago
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    \(\tau = 0\) 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.

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