{
  "abstract": "We prove a structural theorem for point sets in $\\mathbb R^2$ which determine few pinned angles. More precisely, we prove the existence of an absolute constant $c>0$ such that if $n$ is sufficiently large and $P$ is a set of $n$ points then there exists a point $q \\in P$ which determines at least $n^{1+c}$ distinct angles to other pairs of points of $P$, provided that $P$ is not of one of the following exceptional forms: all but at most one of the points of $P$ lie on a line; all but two points of $P$ lie on a line, and the two exceptional points are symmetric with respect to the line; all the points of $P$ lie on a circle; all but one of the points of $P$ lie on a circle, and the exceptional point is the centre of the circle. As a consequence, we answer a question of Corrádi, Erdős and Hajnal by showing that if $n$ is sufficiently large and $P \\subseteq \\mathbb R^2$ has cardinality $n$ and is not contained on a single line, then $P$ determines at least $n-2$ angles. Moreover, we prove that the unique point set attaining this minimum is the regular $n$-gon.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15270",
  "author_total": 3,
  "authors": [
    {
      "name": "Krishnendu Bhowmick"
    },
    {
      "name": "Oliver Roche-Newton"
    },
    {
      "name": "Audie Warren"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bfvfwas5ngg27.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15270",
  "fulltext_url": null,
  "id": "bfvfwas5ngg27",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15270",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7213237640",
  "pdf_url": "https://arxiv.org/pdf/2609.15270",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bfvfwas5ngg27.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.15270",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15270"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Point sets determining few angles are almost contained in a line or circle",
  "title_text": "Point sets determining few angles are almost contained in a line or circle",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/bfvfwas5ngg27",
  "venue": "arXiv",
  "versions": []
}