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@@ -313,12 +313,12 @@ <h1 style="font-size:160%;margin:7px;">How Accurate Are The Conventional Geometr
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A Greek mathematician is credited with refining these approximations through the method of inscribed and circumscribed polygons.
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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.
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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/delta=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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The arcs of the quadrants of a circumscribed circle would meet at the center of the square.
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The arcs of the quadrants that equal in area to the square intersect right between these limits on its centerlines.
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The arcs of the quadrants that equal in area to the square intersect right in between these limits on its centerlines.
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When the arcs of the quadrant circles intersect at the quarter of the centerline of the square, the uncovered area in the middle equals exactly the sum of the overlapping areas respectively.
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