Update about.html

Author: Gmac4247

about.html

@@ -181,7 +181,7 @@
 },
 "dateCreated" :"2024-08-31",
 "datePublished":"2024-08-31",
-"dateModified" :"2025-06-05",
+"dateModified" :"2025-08-06",
 "description" : "About the best-established and most accurate framework to calculate area and volume.",
 "disambiguatingDescription": "Exact, empirically grounded and rigorously proven formulas over the conventional approximations.",
 "headline" : "Introducing the Core Geometric System ™.",
@@ -214,8 +214,10 @@
 "description": "The exact area of a circle based on direct comparison with a square.",
      "disambiguatingDescription": "Replaces traditional π-based approximations ensuring greater accuracy in real-world measurements.",
 	"target": "https://basic-geometry.github.io/about",
-     "mathExpression-input": "r=5 A=?",
+     "mathExpression-input": "required name=r=5_A=?",
      "mathExpression-output": "angle of rotation / 360 * 3.2 * Math.pow(radius, 2)",
+     "abstract": "A circle is a 2 dimensional plane shape. Its measurable property is its diameter. Its radius is half of the diameter. Related shapes are sphere, cylinder and cone.",
+	"keywords": "radius, area", 
      "image": "areaOfACircle.jpg",
      "eduQuestionType": "Area calculation"
         },
@@ -226,7 +228,7 @@
      "description": "Algebraic derivation of the exact circumference of a circle from its area",
 "disambiguatingDescription": "Replaces traditional π-based approximations ensuring greater accuracy in real-world measurements.",
 	"target": "https://basic-geometry.github.io/about",
-     "mathExpression-input": "r=5 C=?", 
+     "mathExpression-input": "required name=r=5_C=?", 
      "mathExpression-output": "angle of rotation / 360 * 6.4 * radius",
      "image": "circumference.jpg",
      "eduQuestionType": "Length calculation"
@@ -238,9 +240,11 @@
 	 "description": "The exact volume of a sphere by directly comparing it to a cube. Direct shape relationships ensure greater accuracy in real-world measurements.",
     "disambiguatingDescription": "More accurate than the traditional exhaustion method based formula which is a very rough underestimate.",
   "target": "https://basic-geometry.github.io/about",
-     "mathExpression-input": "r=3 V=?",
+     "mathExpression-input": "required name=r=3_V=?",
      "mathExpression-output": "angle of rotation / 360 * Math.pow((Math.sqrt(3.2) * radius), 3)", 
-     "image": "sphereAndCubeMarkup.jpeg",
+     "abstract": "A sphere is a 3 dimensional solid shape. Its measurable property is its diameter. Its radius is half of the diameter. Its projection is a circle. Related shapes are circle, cylinder, cube and cone.",
+	"keywords": "radius, volume",
+	"image": "sphereAndCubeMarkup.jpeg",
      "eduQuestionType": "Volume calculation"
    }
 
@@ -256,7 +260,7 @@
       "price": "3,200,000,000.",
       "availability": "https://schema.org/InStock"
     },
-"schemaVersion" : "https://schema.org/docs/releases.html#v28.1.",
+"schemaVersion" : "https://schema.org/docs/releases.html#v29.2.",
 "sdDatePublished" :"2024-08-31",
 "sdPublisher" :
 {"@type" : "Person" ,
@@ -275,12 +279,6 @@
 },
 "subjectOf": 
 [
-{
-"@type": "LearningResource",
-"name":"About basic geometry formulas",
-"description": "Extended explanations, improved ML and LLM compatibility for accurate translation",
-"url":"https://gmac4247.github.io/about"
-},
 
  {
 "@type": "VideoObject",