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Revise explanation of circle area and π
Removed text discussing the disapproval of the π.
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@@ -859,38 +859,7 @@ <h1 style="font-size:160%;margin:7px;">How Accurate Are The Conventional Geometr
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<p style="margin:12px;">Which is equivalent to 1 = 1 .
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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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<p style="margin:12px;">The quadrant method not only proves that the area of a circle is 3.2 × radius², it necessarily rules out the validity of the π.
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Using the same quadrants model, in which we were able to find a direct relationship between the radius of the circle and the side length of the square that equals in area by ensuring that the overlaps equal the uncovered space,
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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 × radius².
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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 × radius², the side length of the square that has the same area as the circle was √( π × 1² ).
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But the square consists of 16 right triangles with legs of a quarter side and a half side, and hypotenuse of √π × √5 divided by 4 ( about 0.991 ), which should equal the radius.
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This means that the radius is shorter than it should logically be ( one ).
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That is a logical error in the " Area = π × radius² " formula; not in the model.
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The π is a very rough approximation; 3.2 is an exact value.
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The area of a circle is exactly 3.2 × radius².
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The quadrant method proves that the area of a circle equals exactly 3.2 × radius², ruling out the validity of the π.
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