{
 "id": "media/karaji-binomial-triangle",
 "class": "media",
 "slug": "karaji-binomial-triangle",
 "label": {
  "ar": "جدول حديث لمعاملات القوى من الصفر إلى الخامسة",
  "en": "Modern coefficient triangle, powers zero to five",
  "ur": "صفر تا پانچ قوتوں کے ضریب کا جدید مثلث"
 },
 "summary": {
  "ar": "رسم حديث من2007 بستة صفوف؛ ليس شاهداً مخطوطاً أو ترميز الكرجي {cite:commons-pascal-triangle-five description}.",
  "en": "Modern2007 drawing with six rows; not a manuscript witness or Karaji's notation {cite:commons-pascal-triangle-five description}.",
  "ur": "2007 کا چھ صفوں والا جدید خاکہ؛ مخطوط شاہد یا کرجی کے رموز نہیں {cite:commons-pascal-triangle-five description}۔"
 },
 "stub": false,
 "wings": [],
 "regions": [],
 "periods": [],
 "tags": [],
 "aliases": [],
 "themes": [],
 "data": {
  "kind": "image",
  "url": "https://upload.wikimedia.org/wikipedia/commons/f/f6/Pascal%27s_triangle_5.svg",
  "license": "CC-BY-SA",
  "creator": "Conrad.Irwin, after Drini",
  "attribution": "Conrad.Irwin, after Drini, Pascal's triangle5.svg, Wikimedia Commons,16 November2007; CC BY-SA3.0 (https://creativecommons.org/licenses/by-sa/3.0/), unchanged.",
  "depicts": [
   "invention/karaji-binomial-coefficient-recurrence"
  ],
  "alt": {
   "ar": "أعداد سوداء في ستة صفوف مثلثة، تبدأ بواحد وتنتهي بصف1،5،10،10،5،1؛ لا أسهم ولا أسماء مؤلفين.",
   "en": "Black numbers in six triangular rows, starting with one and ending1,5,10,10,5,1; no arrows or author names.",
   "ur": "چھ مثلثی صفوں میں سیاہ اعداد، ایک سے شروع اور1،5،10،10،5،1 پر ختم؛ کوئی تیر یا مصنف کا نام نہیں۔"
  },
  "sources": [
   "source/commons-pascal-triangle-five"
  ],
  "provenance": {
   "layer": "own-research",
   "generated_by": "github-copilot",
   "model": "unknown",
   "run": "inventions-p3-b98",
   "source": "Actual540×389 SVG file metadata/history/CC-BY-SA3.0 selector read;960px rendering visually inspected with viewing-only white composite outside git. Museum uses unchanged original SVG, not that composite."
  },
  "status": {
   "review": "published",
   "completeness": 3
  }
 },
 "prose": {},
 "degree": 0,
 "contemporaries": [],
 "updated": "2026-11-07",
 "connections": [],
 "related": [],
 "license": {
  "prose": "CC BY-SA 4.0",
  "data": "CC0 1.0"
 }
}