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.
Pedal curves of conics: an automated exploration of some cubics, sextics, octics and more
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
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.).
citation-role summary
background 1
citation-polarity summary
fields
math.AG 1years
2025 1verdicts
CONDITIONAL 1roles
background 1polarities
unclear 1representative citing papers
citing papers explorer
-
Exploration of offsets of Cayley ovals and their singularities
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.