Resumen de Offsets of a regular trifolium

Thierry Dana-Picard, Zoltán Kovács

• The non-uniqueness of a rational parametrization of a rational plane curve may infiuence the process of computing envelopes of 1-parameter families of plane curves. We study envelopes of family of circles cen-tred on a regular trifolium and its offsets, paying attention to different parametrizations. We use implicitization both to show that two rational parametrizations of a curve are equivalent, and to determine an implicit equation far the envelope under study. The derivation of an implicit equation of an offset follows another path, leading to new developments o/ the package GeoGebra Discovery. As an immediate symbolic result, we obtain that in the general case the offset curve of a regular trifolium is an algebraic curve o/ deg ree 14. We illustrate this fact by providing a GeoGebra a computes such curves automatically and visualizes them in a web browser