Update about.html

Math

Author: Gmac4247

about.html

@@ -231,7 +231,7 @@
 
 radius^2=(a/4)^2)+(2(a/4))^2 
 
-r=sqrt(5)*(a/4)"
+r=5^(1/2)*(a/4)"
     },
     {
       "@type": "HowToStep",
@@ -310,11 +310,11 @@
     {
       "@type": "HowToStep",
       "name": "Comparison Method",
-      "text": "Just as the volume of a cube equals the square root of its cross sectional area cubed - V=(sqrt(Area))^3 -, the volume of a sphere equals the square root of its cross sectional area cubed. 
+      "text": "Just as the volume of a cube equals the square root of its cross sectional area cubed - V=((Area)^(1/2))^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"
+V=((3.2)^(1/2)r)^3"
     }
   ]
    },
@@ -329,12 +329,12 @@
       "@type": "HowToStep",
       "name": "Describing the uncovered and the overlapping areas of the quadrants model algebraically",
       "text": "Quarter of the uncovered area in the middle:
-(sqrt(3.2)r)^2÷4−((90−2×Atan(1÷2))÷360×3.2r^2+2(sqrt(3.2)r÷4×sqrt(3.2)r÷2)÷2))
+((3.2)^(1/2)*r)^2÷4−((90−2×Atan(1÷2))÷360×3.2r^2+2((3.2)^(1/2)*r÷4×(3.2)^(1/2)*r÷2)÷2))
 
 =
 
 An overlapping area: 
-2(Atan(1÷2)÷360×3.2r^2−(sqrt(3.2)r÷4×sqrt(3.2)r÷2)÷2)"
+2(Atan(1÷2)÷360×3.2r^2−((3.2)^(1/2)*r÷4×(3.2)^(1/2)*r÷2)÷2)"
     },
     {
       "@type": "HowToStep",
@@ -364,20 +364,20 @@
 
 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. 
 
-I denoted the radius as 1 and the side as sqrt(π) (sqrt(π*1^2)). It's a logical necessity if the “A=πr^2” formula was right. The side length of the square that has the same area as the circle is sqrt(area of the circle). "
+I denoted the radius as 1 and the side as π^(1/2) ((π*1^2)^(1/2)). It's a logical necessity if the A=πr^2 formula was right. The side length of the square that has the same area as the circle is (area of the circle)^(1/2)."
     },
     {
       "@type": "HowToStep",
       "name": "Verifying the equity between the uncovered and the overlapping areas",
       "text": "π−((90−2×Atan(1÷2))÷360×π+2(π(1÷4×1÷2)÷2))=
 8(Atan(1÷2)÷360×π−π(1÷4×1÷2)÷2) 
 
-The equation holds true, meaning that the overlaps cancel out the unfilled area, so the area of the circle equals the area of the square with side=r*sqrt(π)."
+The equation holds true, meaning that the overlaps cancel out the unfilled area, so the area of the circle equals the area of the square with side=r*π^(1/2)."
     },
     {
       "@type": "HowToStep",
       "name": "Final analysis and conclusion",
-      "text": "The square consists of 16 right triangles with legs of side/4 and side/2 and hypotenuse of sqrt(5)*sqrt(π)÷4~0.991, which equals the radius.
+      "text": "The square consists of 16 right triangles with legs of side/4 and side/2 and hypotenuse of 5^(1/2)*π^(1/2)÷4~0.991, which equals the radius.
 This means that the radius is shorter than it should logically be -one-. 
 
 That's a logical error in the A=πr^2 formula; not the model.