[Step-by-Step] Prove the following biconditional: "The torsion of a space curve is 0 if and only if it is a plane curve." Torsion is defined by (dB)/(ds)=-\tau
Question: Prove the following biconditional: "The torsion of a space curve is 0 if and only if it is a plane curve." Torsion is defined by \(\frac{d\mathbf{B}}{ds}=-\tau \left( s \right)\mathbf{N}\). One can verify that this makes sense (i.e., the derivative of the (unit) binormal with respect to arc length is parallel to the normal), but it is not necessary for you to do so.
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