Torsion: How curves twist in space, and the TNB or Frenet Frame

If you have a curve through space, torsion measures the degree to which the curve "twists". This is separate from how the curve "curves", which we saw was given by the curvature formula. In this video we will study the TNB or Frenet Frame given by three vectors, the Tangent, the principle Normal, and the new vector called the BiNormal vector. The Tangent and Normal Vectors define a plane and what Torsion measures is how that plane changes as you move along the curve.

TYPO: Near the beginning, the Normal Vector should be 1/k dT/ds. I forgot the 1/k, where k is the curvature.


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