Update about.html

Author: Gmac4247

about.html

@@ -286,17 +286,11 @@ <h1 style="font-size:160%;margin:7px;">How Accurate Are The Conventional Geometr
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-<p style="margin:12px;">Historically, Euclidean geometry has provided a framework for understanding and describing the physical world. It is based on axioms and postulates, leading to well-defined formulas for the calculation of areas and volumes of shapes such as circles and spheres.
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-<h2 style="font-size:160%;margin:7px;">Disapproval of the mathematical constant π</h2>
+<p style="margin:12px;">Historically, Euclidean geometry has provided a framework for understanding and describing the physical world. It is based on axioms and postulates, leading to well-defined formulas for the calculation of areas and volumes of shapes such as circles and spheres.
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 <p style="margin:12px;">The constant relationship between a circle's circumference and its diameter has captivated mathematicians for millennia. 
 While its approximate value of 3.14, commonly denoted by the Greek letter π, is widely recognized today, the historical development of this concept is less understood.
 Ancient civilizations grappled with this geometric challenge, employing various methods to approximate this ratio. 
@@ -311,7 +305,7 @@ <h2 style="font-size:160%;margin:7px;">Disapproval of the mathematical constant
 His approach was that the ratio between the perimeter and the diameter of a circle can be estimated by comparing the circumference of the circle to the perimeters of an inscribed and a circumscribed polygon. 
 The polygons can be divided into triangles. The ratio between the legs of the triangles and their hypotenuses can be measured linearly.
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-That is where the pi divided by delta = 3.14 notation might originate from.
+That is where the pi divided by delta ( with delta = 1 ) π ~ 3.14 notation might originate from.
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 This method has several limitations. He tried to increase the accuracy by increasing the number of sides of the polygons. This approach cannot produce an accurate result. 
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 <p style="margin:12px;">The equation can be simplified algebraically.
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 <p style="margin:12px;">Simplifying further:
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 <p style="margin:12px;">Substituting 90° / 360° for 1 / 4 :
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 <p style="margin:12px;">Simplifying further:
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 <p style="margin:12px;">Which is equivalent to 1 = 1 .
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@@ -753,7 +750,7 @@ <h2 style="font-size:160%;margin:7px;">Disapproval of the mathematical constant
 and the radius of the circle equals √5 × quarter of the side, I change the side length of the square to √π, assuming that the area of a circle equals π × ( square value of the radius ). 
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-The idea is that the area of the circle equals to 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. 
+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. 
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 I denoted the radius as 1 and the side as √π, because if the area equaled π × ( square value of the radius ), the side length of the square that has the same area as the circle was √( π × ( square value of 1 ) ). 
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 <p style="margin:12px;">Expand the term (r - x)²:
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 <p style="margin:12px;">Substitute this back into the original expression:
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 <p style="margin:12px;">Distribute the 3.2 inside the parentheses:
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 <p style="margin:12px;">Simplify the numerator:
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 <p style="margin:12px;">Factor out x from the numerator:
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 <p style="margin:12px;">Cancel out the x in the numerator and denominator:
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 As x is close to 0,
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@@ -1049,20 +1053,33 @@ <h2 style="font-size:160%;margin:7px;">Disapproval of the mathematical constant
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 Irrational or not, with an infinitesimally small thickness the circumference practically equals 6.4 × radius.
-That ratio is a real number.
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-There is no reason to substitute it with a sign.
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+Since the ratio can be expressed as a real number, there is no reason to substitute it with any other sign.
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 The best practice is writing it as it is.
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+From a historical perspective the mathematical constant named π is what it is. It's unlikely to change much. 
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+From a scientific perspective they call it irrational for a reason. It doesn't make much sense. It's a logical dead end.
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+The people deserve better than an irrational approximation if an exact calculation is available.
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+That makes sin( π / 2 ) < 1 . That's an aspect of this.
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-<h3 style="margin:6px;">Volume of a sphere</h3>
+<p style="margin:12px;">Another aspect is applying the area relationship in 3D to get the volume of a sphere by cubing the square root of its cross sectional area.
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  <iframe title="The sphere experiment" width="420" height="315" src="https://youtube.com/embed/7uxyLfh2B38">
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-<h4 style="font-size:160%;margin:7px;">Volume of a pyramid</h4>
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+<p style="margin:12px;">The volume of a cone can be derived algebraically by comparing the volume of a quadrant of a vertical frustum cone to an octant of a sphere.
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+The volume of a pyramid can be calculated with the same coefficient. 
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