Primitivoids and inversions of plane curves

TL;DR

This paper explores the concept of primitivoids, which are related to pedals of plane curves, and investigates their properties and relationships, especially around inflection points.

Contribution

It introduces and studies primitivoids as a new class of curves related to pedals and their inverses, expanding the understanding of curve transformations in the plane.

Findings

Primitivoids are closely related to pedal curves of plane curves.

The paper establishes relationships between primitivoids and classical pedal curves.

Singular points of pedals correspond to special features of primitivoids.

Abstract

The pedal of a curve in the Euclidean plane is a classical subject which has a singular point at the inflection point of the original curve. The primitive of a curve is a curve given by the inverse construction for making the pedal. We consider relatives of the primitive of a plane curve which we call primitivoids. We investigate the relationship of primitivoids and pedals of plane curves.