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Curvature and Torsion of a Curve

  1. Curvature: The Curvature of a Curve (denoted by \(\kappa\)) is the Measure of its Bent i.e. the extent to which it Deviates from being a Straight Line The more the Curvature of a Curve at any given Point, the more is the Extent to which it Bends at that Point.

    The Curvature of a Straight Line is 0 at all Points. The Curvature of a Circle with Radius \(R\) is Constant (\(=\Large{\frac{1}{R}}\)) at all Points.
  2. Torsion: The Torsion of a Curve (denoted by \(\tau\)) is the Measure of its Twist i.e. the extent to which it Deviates from being a Curve on a Plane (i.e. Planar Curve). The more the Torsion of a Curve at any given Point, the more is the extent to which it Twisted at that Point.

    The Torsion of a Planar Curve is 0 at all Points. Both the Curvature and Torsion of a Right Circular Helix (also known as Circular Cylindrical Helix) are Constant at all Points.

    Please note that Torsion of a Curve at any Point can be Non Zero only if the Curvature of the Curve is Non Zero at that Point.
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