Update index.html

Author: Gmac4247

index.html

@@ -697,8 +697,8 @@ <h3 itemprop="name">Dividing Fractions</h3>
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-<section id="geometry"">
-<h3>The 2nd and the 3rd Powers manifesting in Geometry</h3>
+<section itemprop="subjectOf" itemscope itemtype="http://schema.org/LearningResource" id="geometry"">
+<h3 itemprop="name">The 2nd and the 3rd Powers manifesting in Geometry</h3>
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 <section itemprop="about" itemscope itemtype="http://schema.org/LearningResource" id="square">
 <h3 itemprop="name">Area of a Square</h3>
@@ -1763,14 +1763,13 @@ <h3 itemprop="eduQuestionType" style="margin:7px">Area of a Circle</h3>
     <img class="center-fit" src="circleArea.png" alt="The circle is cut into four quadrants, each placed with their origin on the vertices of a square. The arcs of the quadrants of the circle that equals in area to the square intersect at the quarters on its centerlines. The ratio between the radius of the circle and the side of the square is calculable. r = side × √5 / 4 Area = 3.2r²">
 </figure>
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-<p itemprop="description" style="margin:12px">The area of a circle is defined by comparing it to a square since that is the base of area calculation.</p>
 <section>
 <details>
-  <summary><h4 itemprop="usageInfo" style="margin:12px"><strong>Direct comparison to a square ensures exactness.</strong></h4></summary>
+  <summary><h4 itemprop="description" style="margin:12px">The area of a circle is defined by comparing it to a square since that is the base of area calculation.</h4></summary>
 <p itemprop="disambiguatingDescription" style="margin:12px"><strong>The widely used formula " A = pi × r² " is not a direct result of calculus. It’s multiplying the approximate circumference formula C = 2pi × r by half the radius, treating the area as the sum of infinitesimal rings. While that method is algebraically valid, it relies on the approximate circumference and bypasses the geometric logic that defines area: the comparison to a square.</strong></p>
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-</section><p itemprop="abstract" style="margin:12px">The circle can be cut into four quadrants, each placed with their origin on the vertices of a square.
+</section><p itemprop="description" style="margin:12px">The circle can be cut into four quadrants, each placed with their origin on the vertices of a square.
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 In this layout the arcs of the quadrants of an inscribed circle would meet at the midpoints of the sides of the square, leaving some of the square uncovered. 
@@ -1893,7 +1892,7 @@ <h3 itemprop="eduQuestionType" style="margin:7px">Area of a Circle</h3>
 </math>
 </div>
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-<section style="margin:12px" id="circle_area_proof">
+<section itemprop="description" style="margin:12px" id="circle_area_proof">
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   <summary><h4>When the overlapping area equals to the uncovered area in the middle, the sum of the areas of the quadrants is equal to the area of the square. That square represents the area of the circle in square units.</h4></summary>
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@@ -2314,7 +2313,7 @@ <h3 itemprop="eduQuestionType" style="margin:7px">Area of a Circle</h3>
 </section>
 <p style="margin:12px" itemprop="description">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.</p>
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-<div style="margin:12px" itemprop="result" itemscope itemtype="https://schema.org/MathSolver">
+<div itemprop="result" itemscope itemtype="https://schema.org/MathSolver">
 <math itemprop="mathExpression" display="block" xmlns="http://www.w3.org/1998/Math/MathML">
 <mrow>
 <mi>A</mi>
@@ -2676,7 +2675,7 @@ <h4>A Rational Alternative: 3.2</h4>
 The length of the two longer sides is the area of the resulting ring divided by x.
 </p>
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-<div style="margin:12px" itemprop="abstract">
+<div itemprop="description">
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@@ -2984,9 +2983,9 @@ <h3 itemprop="eduQuestionType" style="margin:7px">Area of a Circle Segment</h3>
     <img class="center-fit" src="circleSegment.jpg" alt="The area of a circle segment can be calculated by subtracting a triangle from a circle slice. Area = Acos(( r - n ) / r ) × r² - sin( Acos(( r - n ) / r ) × ( r - n ) × r">
     </figure>
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-    <p itemprop="abstract" style="margin:12px">The area of a circle segment can be calculated by subtracting a triangle from a circle slice.</p>
+    <p itemprop="description" style="margin:12px">The area of a circle segment can be calculated by subtracting a triangle from a circle slice.
 <br>
-<p itemprop="description" style="margin:12px">The angle of the slice is given by the ratio between the segment height and the radius of the parent circle. The base of the triangle is the chord, its height is the segment height subtracted from the radius of the parent circle. If the radius of the parent circle is unknown it can be calculated from the the length of the segment ( chord ).</p>
+<br>The angle of the slice is given by the ratio between the segment height and the radius of the parent circle. The base of the triangle is the chord, its height is the segment height subtracted from the radius of the parent circle. If the radius of the parent circle is unknown it can be calculated from the the length of the segment ( chord ).</p>
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 <math style="margin:12px" xmlns="http://www.w3.org/1998/Math/MathML">
   <mi>radius</mi>
@@ -3154,7 +3153,7 @@ <h3 itemprop="eduQuestionType" style="margin:7px">Surface Area of a Cone</h3>
   <img class="center-fit" src="cone.jpeg" alt="The surface area of a cone is calculated as a circle slice with a radius equal to the slant height. Area = 3.2r × ( r + √( r² + H² )">
   </figure>
 <br>
-<p style="margin:12px" itemprop="abstract">The surface area of a cone is calculated as a circle slice with a radius equal to the slant height and the angle given by the ratio between the height and the slant height.</p>
+<p style="margin:12px" itemprop="description">The surface area of a cone is calculated as a circle slice with a radius equal to the slant height and the angle given by the ratio between the height and the slant height.</p>
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 <div style="margin:12px" itemprop="result" itemscope itemtype="https://schema.org/MathSolver">
 <math display="block" itemprop="mathExpression" xmlns="http://www.w3.org/1998/Math/MathML" >
@@ -3238,10 +3237,9 @@ <h3 itemprop="eduQuestionType" style="margin:7px">Volume of a Sphere</h3>
 <figure itemprop="image" class="imgbox" itemscope itemtype="http://schema.org/ImageObject">
     <img class="center-fit" src="sphere.jpeg" alt="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. Volume = ( √ ( 3.2 ) × r )³">
     </figure>
-<p itemprop="description" style="margin:12px"><strong>The volume of a sphere is defined by comparing it to a cube, since that is the base of volume calculation.</strong>
 <section style="margin:12px">
 <details>
-  <summary><h4 itemprop="usageInfo">Direct comparison to a cube ensures exactness.</h4></summary>
+  <summary><h4 itemprop="description">The volume of a sphere is defined by comparing it to a cube, since that is the base of volume calculation.</h4></summary>
 <p itemprop="disambiguatingDescription">The " V = 4 / 3 × pi × radius³ " formula is widely used for the volume of a sphere. 
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@@ -3347,7 +3345,7 @@ <h3 itemprop="name" style="margin:7px">Surface Area of a Sphere</h3>
 Unlock the true formula to calculate the surface area of a sphere.
 </strong>( + tax, if applies )
 </p>
-<meta itemprop="inLanguage" content="en">
+<meta itemprop="isFamilyFriendly" content="true">
 <span itemprop="priceCurrency" content="USD">$</span>
 <span itemprop="price" content="3,200,000,000.00">3,200,000,000.00</span>
 <link itemprop="availability" href="https://schema.org/InStock">