The Twisted Cubic
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Introduction:
The twisted cubic is formed by taking a parabola in the xy plane and bending the ends in the z direction so that the shadow of the curve on the xz plane looks like a cubic. Note that, while the parameterization of the function is extremely simple, its arclength and Frenet frame are complicated.
Definition:
Properties:
Velocity and Acceleration:
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The Frenet Frame:
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Arc Length: |
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Curvature and Torsion:
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