Function Repository Resource:

# CurveTorsion

Compute the torsion of a curve

Contributed by: Wolfram Staff (original content by Alfred Gray)
 ResourceFunction["CurveTorsion"][c,t] computes the torsion of a space curve c parametrized by t.

## Details and Options

Torsion gives a measure of how rapidly a curve deviates from its osculating plane.

## Examples

### Basic Examples (4)

Plot the twisted cubic curve:

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Compute the torsion of the twisted cubic curve:

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Compute the curvature using the resource function Curvature:

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Plot them:

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### Scope (2)

For this curve, the torsion and curvature are the same:

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Plot of the above results:

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A curve that is qualitatively similar to a torus knot:

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Plot the curve:

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Find the torsion:

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Plot this:

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Compute the curvature with the resource function Curvature:

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### Properties and Relations (2)

Define a conical spiral:

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Here is the torsion:

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There are other quantities related to torsion. The inverse of the torsion is called the radius of torsion:

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The curvature, which can be calculated with the resource function Curvature:

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There is also the so-called total curvature:

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Definition of a unit speed helix:

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The curvature, via the resource function Curvature:

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The torsion:

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The relation to the Frenet-Serret system is that the curvature and the torsion are the first two quantities:

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Enrique Zeleny

## Version History

• 1.0.0 – 30 April 2020