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Update about.html
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@@ -744,17 +744,17 @@ <h1 style="font-size:160%;margin:7px;">How Accurate Are The Conventional Geometr
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<p style="margin:12px;">The quadrant method not only proves that the area of a circle is 3.2 × ( square value of the radius ), it necessarily rules out the validity of the π.
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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 unfilled 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 × ( square value of the radius ).
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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 × ( 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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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 × ).
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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 × ( square value of the radius ) " formula; not in the model.
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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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