{
  "abstract": "If a circumscribed conic and an inscribed conic of a triangle are fixed, then, according to Poncelet's porism, there exists a “rotation” of this triangle during which it remains inscribed in the former and circumscribed about the latter. We call such a rotation biconic. The paper presents a number of geometric constructions with inscribed and circumscribed triangles of two conics. Using them, we provide a synthetic proof of Weill’s theorems on biconic rotation induced by a pencil of conics. Then, a more general dynamics of the biconical rotation of the main circumconic of the triangle — the circumscribed conic of the triangle passing through two fixed points — the contacts — is studied. All positions of the contacts are described for which the family $\\mathcal{MC}$ of main circumconics of poristic triangles forms a pencil of conics. It is then shown that for arbitrary contacts, the family $\\mathcal{MC}$ belongs to a certain bundle of conics. In particular, the circumcircles of all poristic triangles have a common radical center. Dual constructions are also presented.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Evgeny A. Avksentyev"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5nnrrbmcxq72a.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "5nnrrbmcxq72a",
  "issns": [],
  "landing_url": "https://hal.science/hal-05838532v1",
  "language": "ru",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-gm"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05838532/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5nnrrbmcxq72a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:01Z",
      "native_id": "hal-05838532",
      "source": "hal",
      "url": "https://hal.science/hal-05838532v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:0.math",
      "subfield": "general"
    }
  ],
  "title": "Biconic rotation of triangles",
  "title_text": "Biconic rotation of triangles",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:01Z",
  "url": "https://research.draconitic.com/paper/5nnrrbmcxq72a",
  "venue": "HAL",
  "versions": []
}