{
  "abstract": "Let s be the semiperimeter of a triangle ABC . Walking the same oriented distance s + ℓ along the boundary from each vertex produces points A 1 ∈ BC , B 1 ∈ C A, C 1 ∈ AB, and we prove the exact identity\n\nwhere R and r are the circumradius and the inradius. It follows from a three-parameter barycentric determinant formula, recovers the equal-perimeter inequality of Aassila and the extension of Torrejón, and exhibits the invariant form of the area computation of Lupu and Spȃtaru. With Blundon's inequality it gives sharp bounds at fixed R and r . We then study the Erdős-Debrunner power-mean inequality along this family. With q = ℓ/s, the optimal exponent is found explicitly for 1/9 ≤ |q| < 1/5, it tends to the unrestricted optimum as q → 0, and as |q| ↑ 1/9 it tends to 1, with a corner at 1/9 and an explicit, super-exponentially small correction to a boundary exponent.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Mohammed Aassila"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8wt1p9dj5x23p.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "8wt1p9dj5x23p",
  "issns": [],
  "landing_url": "https://hal.science/hal-05777110v1",
  "language": "en",
  "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-ca"
    ],
    [
      "hal",
      "1.math.math-mg"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05777110/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8wt1p9dj5x23p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:47Z",
      "native_id": "hal-05777110",
      "source": "hal",
      "url": "https://hal.science/hal-05777110v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-ca",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-mg",
      "subfield": "geometry-topology"
    }
  ],
  "title": "PERIMETER ROTATIONS OF TRIANGLES AND THE ERDŐS-DEBRUNNER INEQUALITY",
  "title_text": "PERIMETER ROTATIONS OF TRIANGLES AND THE ERDŐS-DEBRUNNER INEQUALITY",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:47Z",
  "url": "https://research.draconitic.com/paper/8wt1p9dj5x23p",
  "venue": "HAL",
  "versions": []
}