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The torsion of a space curve measures the rate at which

  • A.the curvature itself changes along the curve
  • B.the curve twists out of its osculating plane
  • C.the tangent direction turns within the osculating plane
  • D.the arc length grows with the parameter

Answer: B

Curvature measures the turning of the tangent, and torsion the turning of the binormal, which is the same as the tilting of the plane containing the tangent and principal normal. A plane curve has zero torsion whatever its curvature, since it never leaves its own plane

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