{
 "id": "source/weisstein-spherical-cap",
 "class": "source",
 "slug": "weisstein-spherical-cap",
 "label": {
  "ar": "وايستين: القطعة الكروية",
  "en": "Weisstein: Spherical Cap",
  "ur": "وائس ٹائن: کروی ٹوپی"
 },
 "summary": {
  "ar": "تعريف وصيغ حديثة لحجم القطعة، لا شاهد على رموز الماهاني.",
  "en": "Modern cap definition and volume formulas, not evidence for al-Mahani's notation.",
  "ur": "کروی حصے کی جدید تعریف و حجم، ماہانی کی علامتوں کا ثبوت نہیں۔"
 },
 "stub": false,
 "wings": [],
 "regions": [],
 "periods": [],
 "tags": [],
 "aliases": [],
 "themes": [],
 "data": {
  "kind": "secondary",
  "type": "article",
  "title": "Spherical Cap",
  "author": [
   {
    "family": "Weisstein",
    "given": "Eric W."
   }
  ],
  "publisher": "MathWorld — A Wolfram Resource",
  "language": "en",
  "URL": "https://mathworld.wolfram.com/SphericalCap.html",
  "open_access": true,
  "reliability_note": "Actual definition and equations2–6 read: V=pi*h*(3a²+h²)/6, a²=2Rh-h² and V=pi*h²*(3R-h)/3. Independent normalized examples/checks are museum calculations, not historical numerical data. No claim that all later sections or cited reference books were studied.",
  "status": {
   "review": "published",
   "completeness": 3,
   "generated_by": "Copilot SDK in VS Code"
  },
  "provenance": {
   "generated_by": "Copilot SDK in VS Code",
   "model": "unknown",
   "run": "inventions-p3-b80",
   "source": "Actual MathWorld definition/formulas, not its copyrighted illustration reused."
  }
 },
 "prose": {},
 "degree": 0,
 "contemporaries": [],
 "updated": "2026-11-06",
 "connections": [],
 "related": [],
 "license": {
  "prose": "CC BY-SA 4.0",
  "data": "CC0 1.0"
 }
}