{
 "id": "source/dennis-addington-alhazen-summation-2009",
 "class": "source",
 "slug": "dennis-addington-alhazen-summation-2009",
 "label": {
  "ar": "صيغ جمع ابن الهيثم — دنيس وأدنغتون2009",
  "en": "Alhazen's Summation Formulas — Dennis/Addington2009",
  "ur": "ابن الہیثم کے جمع کے ضابطے — ڈینس و ایڈنگٹن2009"
 },
 "summary": {
  "ar": "مذكرة تعليمية حديثة بمستطيلات وأشرطة وصيغ مجاميع، مع تمييز نسب الحجوم من الرموز الحديثة.",
  "en": "Modern rectangle/strip teaching reconstruction and power-sum formulas, distinguishing volume ratios from modern notation.",
  "ur": "مستطیلوں و پٹیوں سے جدید تدریسی تشکیل اور قوتوں کے ضابطے؛ حجم کی نسبت و جدید علامتیں الگ۔"
 },
 "stub": false,
 "wings": [],
 "regions": [],
 "periods": [],
 "tags": [],
 "aliases": [],
 "themes": [],
 "data": {
  "kind": "secondary",
  "type": "article",
  "title": "Alhazen's Summation Formulas",
  "author": [
   {
    "family": "Dennis",
    "given": "David"
   },
   {
    "family": "Addington",
    "given": "Susan"
   }
  ],
  "publisher": "Quadrivium, Mathematical Intentions, five-page teaching notes",
  "issued": {
   "date-parts": [
    [
     2009
    ]
   ]
  },
  "language": "en",
  "URL": "https://quadrivium.info/MathInt/Notes/AlHazenSummation.pdf",
  "open_access": true,
  "reliability_note": "Actual five-page PDF read;2009 copyright/byline verified. Modern pedagogical rectangle/strip and volume reconstruction, citing Edwards1979, not Arabic edition. Geometric ratios distinguished from modern polynomial formulas; extendability of recurrence not evidence author proved every power. Figures/text remain outside git; licence is not an open media licence.",
  "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-b36",
   "source": "Actual downloaded five-page teaching PDF and copyright/byline"
  }
 },
 "prose": {},
 "degree": 0,
 "contemporaries": [],
 "updated": "2026-11-06",
 "connections": [],
 "related": [],
 "license": {
  "prose": "CC BY-SA 4.0",
  "data": "CC0 1.0"
 }
}