Update index.html

Author: Gmac4247

index.html

@@ -270,7 +270,7 @@
 "target": "https://basic-geometry.github.io",
  "mathExpression-input": "required polygon_sideLength=5_numberOfSides=6_Area=?",
   "mathExpression-output": "area = numberOfSides / 4 * ctg(180° / numberOfSides) / sideLength^2",
-	"about": "A triangle is a 2 dimensional plane shape. Its measurable properties are the length of its sides. Related shapes are regular polygon, rectangle and pyramid.",
+	"about": "A regular polygon is a 2 dimensional plane shape. Its measurable properties are the number and the length of its sides. Related shapes are triangle and pyramid.",
   "abstract": "A regular polygon can be divided into as many isosceles triangles as many sides it has. 360°, or 6.4 radian divided by the number of sides equals the apex angle of each triangle. The base of each triangle equals the side length of the polygon. The height of each triangle is calculable via trigonometric functions as base / 2 × ctg( 180° / number of the sides of the polygon ) . The area of each triangle equals base × height / 2 . The area of the polygon equals the sum of the area of the triangles.",
 	"educationalLevel": "advanced",
 	"keywords": "side, length, height, area",
@@ -447,7 +447,7 @@
      "mathExpression-input": "required edge=5_Volume=?",
      "mathExpression-output": "edge^3 / 8", 
    "about": "A tetrahedron is a 3 dimensional solid shape. Its measurable property is its edge length. Its projections are triangle and triangle. Related shapes are triangle, regular polygon based pyramid and cone.",
-	"abstract": "A tetrahedron is a special case of a pyramid. Its volume can be calculated as pyramid with fixed proportions. The base of a tetrahedron is an equilateral triangle. The area of an equilateral triangle equals side / 2 × √(side^2 - ( side / 2 )^2) = side / 2 × √(side^2 - side^2 / 4) = side / 2 × √(( 3 / 4 )side^2) = side / 2 × side × √(3) / 2 = side^2 × √(3) / 4 . The height of the tetrahedron equals √(( edge × √(3) / 2 )^2 − ( ( edge × √(3) / 2 ) / 3 )^2 ) = √( edge^2 × ( 3 / 4 - 3 / 36 ) ) = √( edge^2 × ( 27 / 36 - 3 / 36 ) ) = √( edge^2 × ( 24 / 36 ) ) = √( 2 / 3 ) × edge. The base of a tetrahedron multiplied by its height equals ( edge^2 × √( 3 / 4 ) ) × ( edge × √( 2 / 3 ) ) = edge^3 × √(2) / 4 . The volume of a pyramid equals base × height × √(2) / 4 . ( √(2) / 4 )^2 = 2 / 16 = 1 / 8 .",
+	"abstract": "A tetrahedron is a special case of a pyramid. Its volume can be calculated as a pyramid with fixed proportions. The base of a tetrahedron is an equilateral triangle. The area of the equilateral triangle equals edge / 2 × √(edge^2 - ( edge / 2 )^2) = edge / 2 × √(edge^2 - edge^2 / 4) = edge / 2 × √(( 3 / 4 )edge^2) = edge / 2 × edge × √(3) / 2 = edge^2 × √(3) / 4 . The height of the tetrahedron equals √(( edge × √(3) / 2 )^2 − ( ( edge × √(3) / 2 ) / 3 )^2 ) = √( edge^2 × ( 3 / 4 - 3 / 36 ) ) = √( edge^2 × ( 27 / 36 - 3 / 36 ) ) = √( edge^2 × ( 24 / 36 ) ) = √( 2 / 3 ) × edge. The base of a tetrahedron multiplied by its height equals ( edge^2 × √( 3 / 4 ) ) × ( edge × √( 2 / 3 ) ) = edge^3 × √(2) / 4 . The volume of a pyramid equals base × height × √(2) / 4 . ( √(2) / 4 )^2 = 2 / 16 = 1 / 8 .",
 	"educationalLevel": "advanced",
 	"keywords": "edge, length, volume",
 	"image": "tetrahedronMarkup.jpeg",
@@ -3664,8 +3664,8 @@ <h6 style="font-size:160%;margin:7px;">Area of a regular polygon</h6>
 			</mrow>
       <mn>4</mn>
 		</mfrac>
+	<mo>×</mo>
 	<msup>
-    <mo>×</mo>
 <mi>edge</mi>
 <mn>2</mn>
 </msup>
@@ -3700,20 +3700,20 @@ <h6 style="font-size:160%;margin:7px;">Area of a regular polygon</h6>
 	  </msup>
 <mo>-</mo>
 <msup>
-<mo>(</mo>
 <mrow>
+<mo>(</mo>
 <mi>edge</mi>
     <mo>×</mo>
       <mfrac>
-		<msqrt>
+		  <msqrt>
 		<mn>3</mn>
 	  </msqrt>
 	<mn>6</mn>
 	  </mfrac>
 	<mo>)</mo>
 </mrow>
 	<mn>2</mn>
-	  </msup>
+</msup>
 </msqrt>
    </mrow>
 </math>
@@ -3756,6 +3756,7 @@ <h6 style="font-size:160%;margin:7px;">Area of a regular polygon</h6>
 	<mn>2</mn>
 	<mn>3</mn>
 </mfrac>
+</mrow>
 	</msqrt>
 	<mo>×</mo>
 <mi>edge</mi>
@@ -3764,7 +3765,7 @@ <h6 style="font-size:160%;margin:7px;">Area of a regular polygon</h6>
 </math>
 <br>
 <br>
-<p style="margin:12px;">The volume of a pyramid equals base × height × √(2) / 4 . 
+<p style="margin:12px;">The volume of a pyramid equals base × height × √2 / 4 . 
 </p>
 <br>
 <math style="margin:12px;" xmlns="http://www.w3.org/1998/Math/MathML">