Update about.html

Author: Gmac4247

about.html

@@ -171,7 +171,7 @@
 },
 "dateCreated" :"2024-08-31",
 "datePublished":"2024-08-31",
-"dateModified" :"2025-01-31",
+"dateModified" :"2025-02-01",
 "description" :"History and detailed disapproval of the mathematical constant π; definition and derivation of the properties of shapes from the area of a circle.",
 "disambiguatingDescription": "Exact formulas. No pi.",	
 	"image":[
@@ -312,10 +312,25 @@ <h1 style="font-size:160%;margin:7px;">How Accurate Are The Conventional Geometr
 Ancient civilizations grappled with this geometric challenge, employing various methods to approximate this ratio. 
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 <br>
-A Greek mathematician is credited with refining these approximations through the method of in- and circumscribed polygons.
-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 in- and a circumscribed polygon. The polygons can be divided into triangles. The ratio between the triangles' legs and their hypotenuses can be measured linearly.
-That's where the pi/delta=3.14... denotation might originate from.
-This method has several limitations. He tried to increase the accuracy by increasing the number of the sides of the polygons. This approach cannot yield an accurate result. 
+A Greek mathematician is credited with refining these approximations through the method of inscribed and circumscribed polygons.
+
+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.
+
+That is where the pi/delta=3.14... notation might originate from.
+
+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. 
+
+The same coefficient was used to calculate the ratio between the squared radius and the area of a circle.
+Despite these early advances, a precise, universally accepted value of this constant remained elusive for centuries. 
+
+With its value believed to be an infinite fraction, it seemed necessary to denote it by a sign in the equations.
+
+It was not until the 18th century that the symbol π, popularized by the mathematicians of the time, gained widespread acceptance.
+
+Several complex formulas were introduced by different mathematicians, aimed at more accurately estimating this ratio, based on a theoretical polygon with an infinite number of sides. 
+
+All of the comparison methods mentioned above have one thing in common. They are estimating the perimeters of polygons and do not account for the curved shape of the circle.
 <br>
 <br>
 The same coefficient was used to calculate the ratio between the squared radius and the area of a circle.