Pedal curves of conics: an automated exploration of some cubics, sextics, octics and more

Thierry Dana-Picard

Pedal curves of conics: an automated exploration of some cubics, sextics, octics and more

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arxiv 2503.15135 v1 pith:DYOSXXP6 submitted 2025-03-19 math.AG

Thierry Dana-Picard This is my paper · ORCID

classification math.AG

keywords curvesautomatedconicsexplorationexploreocticspedalsextics

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Constructions and exploration of plane algebraic curves has received a new push with the development of automated methods, whose algorithms are continuously improved and implemented in various software packages. We use them to explore the pedal curves of conics. This provides a construction of interesting geometric loci, given at first by parametric representations. After implicitization, they appear as sextics, octics and other curves of higher degree. We explore their irreducibility and their singular points (crunodes, cusps, etc.).

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Exploration of offsets of Cayley ovals and their singularities
math.AG 2025-05 conditional novelty 6.0 of 10

This exploration shows that offsets of Cayley ovals, though derived from smooth curves, develop cusps and self-intersections whose topology changes as the offset distance increases.

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