## An Equation for the Curvature of a Curve in Terms of Derivatives

Theorem

If a curve in space is given asandthen the curvatureis given by

Proof

hence

Thensince

Sinceandthe binormal vector, we have

Since

Theorem

If a curve in space is given asandthen the curvatureis given by

Proof

hence

Thensince

Sinceandthe binormal vector, we have

Since