Function Repository Resource:

TurningNumber

Compute the turning number of a curve

Contributed by: Wolfram Staff (original content by Alfred Gray)
 ResourceFunction["TurningNumber"][c,{t,a,b}] computes the turning number of a curve c with parameter t running from a to b.

Details and Options

ResourceFunction["TurningNumber"] is similar to winding number, but in this case the number of rotations is counted with respect to the tangent vector of the curve instead of a fixed point.

Examples

Basic Examples (1)

The turning number changes its sign depending on whether the tangent vector moves clockwise or counterclockwise:

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Scope (2)

Define a limaçon:

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Here is a function for computing tangent vectors:

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Interactively plot the limaçon while tracking a tangent vector and its turning number. This shows that the turning number of a limaçon is 2:

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Define an eight curve:

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The turning number of an eight curve is first -1, then 1, giving a total of 0:

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Enrique Zeleny

Version History

• 1.0.0 – 21 February 2020