Function Repository Resource:

EvoluteCurve

Compute the evolute of a curve

Contributed by: Wolfram Staff (original content by Alfred Gray)
 ResourceFunction["EvoluteCurve"][c,t] computes the evolute of the curve c.

Details

An evolute is the locus of the centers of curvature of a plane curve, or the envelope of a plane curve's normals.

Examples

Basic Examples (3)

Define the curve of an ellipse:

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Compute its evolute:

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Plot the ellipse and evolute:

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Define a curve known as a tractrix:

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Its evolute is a catenary:

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Plot the result:

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Define a curve called a cissoid:

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Plot repeated evolutes of the curve:

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Applications (2)

Evolute of a cycloid:

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A cycloidal pendulum, which exhibits the tautochrone property:

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Properties and Relations (1)

The evolute of a curve can be expressed in terms of the curvature and the normal vector:

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Neat Examples (1)

Show the evolute as an envelope of normals:

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Enrique Zeleny

Version History

• 1.0.1 – 08 March 2021
• 1.0.0 – 03 March 2020