# Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

Compute the curve of aberrancy of a plane curve

Contributed by:
Jan Mangaldan

ResourceFunction["AberrancyCurve"][ computes the curve of aberrancy of the plane curve |

The curve of aberrancy is also known as the affine evolute.

The curve of aberrancy is the envelope of the lines that are parallel to the axes of a plane curve's osculating parabolas and pass through their point of contact with the plane curve.

The curve of aberrancy is the locus of the centers of aberrancy of a plane curve.

Define the parametric equations for an astroid:

In[1]:= |

Compute its curve of aberrancy:

In[2]:= |

Out[2]= |

Plot the astroid and its curve of aberrancy:

In[3]:= |

Out[3]= |

Compute the implicit equation for the curve of aberrancy of a quartic:

In[4]:= |

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The curve of aberrancy of a plane curve involves third and fourth derivatives:

In[5]:= |

Out[5]= |

- 1.0.0 – 04 March 2021

This work is licensed under a Creative Commons Attribution 4.0 International License