Update about.html

Author: Gmac4247

about.html

@@ -342,7 +342,7 @@ <h1 style="font-size:160%;margin:7px;">How Accurate Are The Conventional Geometr
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 This narrowing gap was key. Archimedes likely believed that as the number of sides increased, the difference between the perimeters of the inscribed and circumscribed polygons would converge toward zero, approaching the circumference of the circle.
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-He assumed that more sides mean closer resemblance to a circle. That was backed by the isoperimetric inequality, which states that a circle maximizes area for a given perimeter. That idea likely emerged from observing simple polygons: the triangle has the smallest area, the square is larger, and so on. From this pattern, it was assumed that the trend continues indefinitely — that a polygon with an infinite number of sides would resemble a circle perfectly, with its area approaching from below.
+He assumed that more sides mean closer resemblance to a circle. That was backed by the isoperimetric inequality theory, which states that a circle maximizes area for a given perimeter. That idea likely emerged from observing simple polygons: the triangle has the smallest area, the square is larger, and so on. From this pattern, it was assumed that the trend continues indefinitely — that a polygon with an infinite number of sides would resemble a circle perfectly, with its area approaching from below.
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 But that assumption ignores a crucial geometric reality: as the number of sides increases, the internal angles of the polygon approach 180° — it is 180° - 360° / 96 = 176.25° in the case of a 96-gon —, nearing a straight line rather than a curve. In contrast, polygons with internal angles in the range between 150° and 160°, such as the 13- to 16-gon, preserve a meaningful bend that better reflects circularity.