Update about.html

Markup

Author: Gmac4247

about.html

@@ -69,7 +69,7 @@
 
 </style>
 <meta name="viewport" content="width=device-width, initial-scale=1.0, maximum-scale=1.0">
-<meta name="description" content="Introducing the best-established and most accurate framework to calculate area and volume.">
+<meta name="description" content="About the best-established and most accurate framework to calculate area and volume.">
 <meta name="author" content="type=PostalAddress,
   addressLocality=Szentendre,
   addressRegion=Hungary,
@@ -93,7 +93,7 @@
   telephone=+36305075125,
   url=https://www.x.com/gmac4247">
 <meta name="twitter:title" content="About Basic Geometry Formulas">
-<meta name="twitter:description" content="Introducing the best-established and most accurate framework to calculate area and volume.">
+<meta name="twitter:description" content="About the best-established and most accurate framework to calculate area and volume.">
 <meta name="twitter:image" content="android-chrome-256x256.png">
 <script type="application/ld+json" async>
 {
@@ -173,9 +173,9 @@
 },
 "dateCreated" :"2024-08-31",
 "datePublished":"2024-08-31",
-"dateModified" :"2025-05-26",
-"description" : "Introducing the best-established and most accurate framework to calculate area and volume.",
-"disambiguatingDescription": "Providing precise formulas based on empirical considerations and fundamental relationships instead of the conventional approximations.",	
+"dateModified" :"2025-05-27",
+"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.",	
 	"image":[
 	"equityFigure.jpg",
 	"recycle.png",
@@ -194,14 +194,19 @@
 {
 "@type": ["MathSolver", "LearningResource"],
  "name" : "Core Geometric System ™",
- "inLanguage":"en-us",
+"description":"The best-established, empirically grounded, rigorously proven and most accurate framework."
+ "disambiguatingDescription": "Exact formulas over the traditional approximations. More accurate for real-world applications.",
+"keywords":"Exact Formulas, Area of a Circle, Circumference of a Circle, Volume of a Sphere", 
+"inLanguage":"en-us",
  "potentialAction": [
 
 {
      "@type": "SolveMathAction",
-	"name": "Area of a circle",
-"description": "Calculates the exact area of a circle using a refined approach that replaces traditional π-based approximations. This method is based on direct shape relationships, ensuring greater accuracy in real-world measurements.",
-     "target": "https://basic-geometry.github.io/about/",
+	"name": "Area of a Circle",
+"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.",
+	"keywords":"Exact Area of a Circle, Direct Comparison, Quadrants Method, Rigorously Proven",
+	"target": "https://basic-geometry.github.io/about/",
      "mathExpression-input": "r=5 A=?",
      "mathExpression-output": "angle of rotation / 360 * 3.2 * Math.pow(radius, 2)",
      "image": "areaOfACircle.jpg",
@@ -210,8 +215,10 @@
 
 {
      "@type": "SolveMathAction",
-"name": "Circumference of a circle",
+"name": "Circumference of a Circle",
      "description": "Calculates the exact circumference of a circle using a refined approach that replaces traditional π-based approximations. This method is based on direct shape relationships, ensuring greater accuracy in real-world measurements.",
+"disambiguatingDescription": "Replaces traditional π-based approximations ensuring greater accuracy in real-world measurements.",
+	"keywords":"Circumference of a Circle, Algebraic Derivation from the Area, Rigorously Proven",
 	"target": "https://basic-geometry.github.io/about/",
      "mathExpression-input": "r=5 C=?", 
      "mathExpression-output": "angle of rotation / 360 * 6.4 * radius",
@@ -222,8 +229,10 @@
 {
      "@type": "SolveMathAction",
 	"name": "Volume of a sphere",
-	 "description": "Calculates the exact volume of a sphere by directly comparing it to a cube. This method is based on direct shape relationships, ensuring greater accuracy in real-world measurements.",
-     "target": "https://basic-geometry.github.io/about/",
+	 "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.
+	"keywords" : "Direct Comparison, Exact Volume, Rigorously proven",
+  "target": "https://basic-geometry.github.io/about/",
      "mathExpression-input": "r=3 V=?",
      "mathExpression-output": "angle of rotation / 360 * Math.pow((Math.sqrt(3.2) * radius), 3)", 
      "image": "sphereAndCubeMarkup.jpeg",
@@ -1216,7 +1225,7 @@ <h5 style="font-size:160%;margin:7px;">Disapproval of the mathematical constant
 <p style="margin:12px;">The idea is that the area of the circle equals the area of the square. Looking for the ratio between the length of the side, I could denote the side of the square as 1, and compare the radius to that, or denote the radius as 1 and express the side compared to that. 
 <br>
 <br>
-I denoted the radius as 1 and the side as √π, because if the “A=πr²” formula was true, the side length of the square that has the same area as the circle was 
+I denoted the radius as 1 and the side as √π, because if the A=πr² formula was true, the side length of the square that has the same area as the circle was 
 <math xmlns="http://www.w3.org/1998/Math/MathML" >
 <mrow>
 <msqrt>
@@ -1368,7 +1377,7 @@ <h5 style="font-size:160%;margin:7px;">Disapproval of the mathematical constant
 This means that the radius is shorter than it should logically be -one-. 
 <br>
 <br>
-That's a logical error in the "A=πr²" formula; not the model.
+That is a logical error in the A=πr² formula; not the model.
 <br>
 <br>
 The π is a very rough approximation; 3.2 is an exact value.