Update index.html

Text

Author: Gmac4247

index.html

@@ -265,8 +265,8 @@
 "target": "https://basic-geometry.github.io",
  "mathExpression-input": "required triangle_base=5_height=2_Area=?",
   "mathExpression-output": "Area = base * height / 2",
-   "about": "The area of a triangle equals exactly the half of the area of a rectangle with a width equal to the base of the triangle and length equal to the height of the triangle.",
-  "abstract": "A triangle is a 2 dimensional plane shape with 3 straight sides. The base of a triangle multiplied by its height equals to a rectangle with an area exactly the double of the triangle. The square root of half of the area of the rectangle is the side length of the theoretical square that has the same area as the triangle.",
+   "about": "The area of a triangle equals half of the area of a rectangle with a width equal to the base of the triangle and length equal to the height of the triangle.",
+  "abstract": "A triangle is a 2 dimensional plane shape with 3 straight sides. The base of a triangle multiplied by its height equals to a rectangle with twice the area of the triangle. The square root of half of the area of the rectangle is the side length of the theoretical square that has the same area as the triangle.",
 	"educationalLevel": "basic",
 	"keywords": "triangle area, geometry",
     "image": "trigonometry.png",
@@ -339,12 +339,12 @@
 	"target": "https://basic-geometry.github.io",
 "mathExpression-input": "required circle_radius=5_Circumference=?", 
      "mathExpression-output": "Circumference = 6.4 * radius",
-    "about": "The circumference of a circle can be derived from its area algebraically by subtracting the area of a circle from a larger one and dividing the area of the resulting ring by the undefined difference between their radii.",
+    "about": "The circumference of a circle can be derived from its area algebraically by subtracting the area of a smaller circle from it and dividing the difference by the difference of the radii.",
 	"abstract": "The x represents the theoretical width of the circumference, which is a very small number. 
 The difference between the shape of the straightened circumference and a quadrilateral is negligible. 
 The length of the 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=3.2(r^2-(r-x)^2)/x=6.4r-x The length of the circumference approaches 6.4 × radius as the thickness approaces 0.",
+C=3.2(r^2-(r-x)^2)/x=6.4r-x The length of the circumference approaches 6.4 × radius as its thickness approaches 0.",
 	"keywords": "exact circumference, radians, geometry",
 	"educationalLevel": "advanced",
 	"image": "circumference.jpg",
@@ -1808,10 +1808,10 @@ <h2 style="margin:7px">Trigonometry</h2>
 <section id="triangle">
 <h3 style="margin:7px">Area of a Triangle</h3>
 <br>
-<p style="margin:12px">The area of a triangle equals exactly the half of the area of a rectangle with a width equal to the base of the triangle and length equal to the height of the triangle.
+<p style="margin:12px">The area of a triangle equals half of the area of a rectangle with a width equal to the base of the triangle and length equal to the height of the triangle.
 <br>
 <br>
-The base of a triangle multiplied by its height equals to a rectangle with an area exactly the double of the triangle. 
+The base of a triangle multiplied by its height equals to a rectangle with twice the area of the triangle. 
 <br>
 <br>
 The square root of half of the area of the rectangle is the side length of the theoretical square that has the same area as the triangle. 
@@ -2809,7 +2809,7 @@ <h3 style="margin:7px">Circumference of a Circle</h3>
     <img class="center-fit" src="circumference.jpg" alt="figure-Circumference=6.4r">
     </div>
 <br>
-<p style="margin:12px">The circumference of a circle is derived from its area algebraically by subtracting the area of a circle from a larger one and dividing the area of the resulting ring by the undefined difference between their radii. 
+<p style="margin:12px">The circumference of a circle is derived from its area algebraically by subtracting a smaller circle and dividing the difference by the difference of the radii. 
 <br>
 <br>
 The x represents the theoretical width of the circumference, which is a very small number.
@@ -3032,7 +3032,7 @@ <h3 style="margin:7px">Circumference of a Circle</h3>
 </div>
 <br>
 <br>	
-<p style="margin:12px">The length of the circumference approaches 6.4 × radius as its thickness approaces 0.
+<p style="margin:12px">The length of the circumference approaches 6.4 × radius as its thickness approaches 0.
 </p>
 <br>
 <math style="margin:12px" xmlns="http://www.w3.org/1998/Math/MathML">