{
 "id": "source/mathworld-alhazen-problem",
 "class": "source",
 "slug": "mathworld-alhazen-problem",
 "label": {
  "ar": "ماث وورلد — مسألة ابن الهيثم",
  "en": "MathWorld — Alhazen's billiard problem",
  "ur": "میتھ ورلڈ — مسئلۂ ابن الہیثم"
 },
 "summary": {
  "ar": "تعريف المسألة والمقابلات الهندسية وذكر بطليموس والمراجع؛ ليس قراءة لأصول بطليموس أو صبره.",
  "en": "Problem, geometric equivalents, Ptolemy attribution and references; not direct reading of Ptolemy or Sabra.",
  "ur": "مسئلہ، ہندسی مماثلتیں، بطلیموس کی نسبت اور مراجع؛ بطلیموس یا صبرہ کا اصل مطالعہ نہیں۔"
 },
 "stub": false,
 "wings": [],
 "regions": [],
 "periods": [],
 "tags": [],
 "aliases": [],
 "themes": [],
 "data": {
  "kind": "tertiary",
  "type": "article",
  "title": "Alhazen's Billiard Problem",
  "author": [
   {
    "family": "Weisstein",
    "given": "Eric W."
   }
  ],
  "publisher": "Wolfram MathWorld",
  "language": "en",
  "URL": "https://mathworld.wolfram.com/AlhazensBilliardProblem.html",
  "open_access": true,
  "reliability_note": "Actual full page/problem/history/reference list read6 November2026. Reputable tertiary mathematical exposition, not primary historical text. Earlier Ptolemy formulation attributed through this page; its precise150 AD date not adopted as independently verified. General constructibility limitation distinguished from easy special cases. References discovered, not all read.",
  "status": {
   "review": "published",
   "completeness": 2,
   "generated_by": "Copilot SDK in VS Code"
  },
  "provenance": {
   "generated_by": "Copilot SDK in VS Code",
   "model": "unknown",
   "run": "inventions-p3-b50",
   "source": "Actual MathWorld page, not search synthesis; linked references not silently treated as read."
  }
 },
 "prose": {},
 "degree": 0,
 "contemporaries": [],
 "updated": "2026-11-06",
 "connections": [],
 "related": [],
 "license": {
  "prose": "CC BY-SA 4.0",
  "data": "CC0 1.0"
 }
}