Update about.html

Added step by step explanation to math solver markup

Author: Gmac4247

about.html

@@ -173,7 +173,7 @@
 },
 "dateCreated" :"2024-08-31",
 "datePublished":"2024-08-31",
-"dateModified" :"2025-05-24",
+"dateModified" :"2025-05-25",
 "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.",	
 	"image":[
@@ -207,8 +207,41 @@
        "additionalProperty": {
        "@type": "PropertyValue",
        "name": "Formula",
-       "value": "angleOfRotation / 360 * 3.2 * Math.pow(radius, 2)"
-  }
+       "value": "angleOfRotation / 360 * 3.2 * Math.pow(radius, 2)",
+},
+	 "description": "Calculates the exact area of a circle using a refined approach that replaces traditional π-based methods. This method is based on direct shape relationships, ensuring greater accuracy in real-world measurements.",
+	"stepByStepInstructions": [
+    {
+      "@type": "HowToStep",
+      "name": "Define Square Comparison",
+      "text": "A circle's area is determined by comparing it to a square. The circle is divided into four quadrants, each positioned at the vertices of the square."
+    },
+    {
+      "@type": "HowToStep",
+      "name": "Equalize Overlaps and Unfilled Space",
+      "text": "The arcs of the quadrants of an inscribed circle would meet at the midpoints of the sides of the square. 
+
+The arcs of the quadrants of a circumscribed circle would meet at the center of the square.
+
+When the arcs of the quadrant circles intersect at the quarter of the centerline of the square, the uncovered area in the middle equals exactly the sum of the overlapping areas respectively."
+    },
+    {
+      "@type": "HowToStep",
+      "name": "Relating the Radius to the Side of the Square",
+      "text": "The ratio between the radius of the circle and the side of the square can be calculated by using the Pythagorean theorem.
+
+r²=(a/4)²+(2(a/4))² 
+
+r=(√5)(a/4)"
+    },
+    {
+      "@type": "HowToStep",
+      "name": "Express the Area in Terms of the Radius",
+      "text": "The area of both the square and the sum of the quadrants equals 16 right triangles with legs of a quarter and a half of the square's sides, and its hypotenuse equal to the radius of the circle. 
+
+A=(16/5)r²=3.2r²"
+    }
+  ]
    },
 
 {
@@ -223,7 +256,36 @@
        "@type": "PropertyValue",
        "name": "Formula",
        "value": "angleOfRotation / 360 * 6.4 * radius"
-  }
+  },
+	 "description": "Calculates the exact circumference of a circle using a refined approach that replaces traditional π-based methods. This method is based on direct shape relationships, ensuring greater accuracy in real-world measurements.",
+  "stepByStepInstructions": [
+    {
+      "@type": "HowToStep",
+      "name": "Define the Circumference based on the Area",
+      "text": "The circumference of a circle is derived algebraically from its area by subtracting a theoretical circle, with a radius shorter than the radius of the actual circle by the theoretical width of the circumference."
+    },
+    {
+      "@type": "HowToStep",
+      "name": "Give the Circumference a theoretical Width",
+      "text": "The x represents the width of the circumference, which is just theoretical, hence a very small number."
+    },
+    {
+      "@type": "HowToStep",
+      "name": "Compare the Circumference to a quadrilateral",
+      "text": "The difference between the shape of the straightened circumference and a quadrilateral is negligible. 
+
+The length of two shorter sides of the quadrilateral is x.
+
+The length of the two longer sides is the area of the resulting ring divided by x.
+
+C=(3.2r²-3.2(r-x)²)/x=6.4r-3.2x"
+    },
+    {
+      "@type": "HowToStep",
+      "name": "Subtract the theoretical Width",
+      "text": "As x is close to 0, C=6.4r"
+    }
+  ]
    },
 
 {
@@ -238,7 +300,24 @@
        "@type": "PropertyValue",
        "name": "Formula",
        "value": "angleOfRotation/360*(3.2^(1/2)*radius)^3"
-  }
+  },
+	 "description": "Calculates the exact volume of a sphere using a refined approach that replaces traditional exhaustion method. This method is based on direct shape relationships, ensuring greater accuracy in real-world measurements.",
+  "stepByStepInstructions": [
+    {
+      "@type": "HowToStep",
+      "name": "Define Cube Comparison",
+      "text": "The volume of a sphere is defined by comparing it to a cube, as that's the base of volume calculation."
+    },
+    {
+      "@type": "HowToStep",
+      "name": "Comparison Method",
+      "text": "Just as the volume of a cube equals the square root of its cross sectional area cubed - V=(√(A))³ -, the volume of a sphere equals the square root of its cross sectional area cubed. 
+
+The edge length of the cube, which has the same volume as the sphere, equals the square root of the area of the square that has the same area as the sphere's cross section.
+
+V=(√(3.2)r)³"
+    }
+  ]
    }
 ],
 "url": "https://basic-geometry.github.io/about/",