Pedal curves of conics: an automated exploration of some cubics, sextics, octics and more
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | |
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| _version_ | 1866912283014201344 |
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| author | Dana-Picard, Thierry |
| author_facet | Dana-Picard, Thierry |
| contents | 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.). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15135 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pedal curves of conics: an automated exploration of some cubics, sextics, octics and more Dana-Picard, Thierry Algebraic Geometry 97G40, 14H50 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.). |
| title | Pedal curves of conics: an automated exploration of some cubics, sextics, octics and more |
| topic | Algebraic Geometry 97G40, 14H50 |
| url | https://arxiv.org/abs/2503.15135 |