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@@ -314,9 +314,21 @@ <h1 style="font-size:160%;margin:7px;">About the Core Geometric System ™</h1>
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Meanwhile I got curious about the properties of other shapes, and I figured that the volume of a sphere equals the cubed value of the square root of its cross-sectional area, just like a cube.
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With the limited resources that I had, I conducted some experiments. I could not provide the accuracy that the subject deserves, but the results aligned with my V=(√(3.2)r)³ formula better than the conventional "4 / 3 × π × r³".
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It's quite hard to physically measure the volume of a ball accurately, but there's a significant difference between the result of my V=(√(3.2)r)³ formula and the conventional "4 / 3 × π × r³".
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It's quite hard to physically measure the volume of a ball accurately, but there's a significant difference between the results of these two formulas, that was easy to see.
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With the limited resources that I had, I conducted some experiments.
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The subject of the sphere experiment was a standard golf ball. That is not a perfect sphere because there are dimples on its surface. That can be compensated by calculating with a slightly shorter radius.
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The measuring bottle had a nominal volume of 4 cl (40 ml ~ 1.3526 US ounce). That is not perfectly precise either because the nominal volume indicates the guaranteed amount of the fluid in it in commerce. They come with an air gap atop the fluid so the total capacity of the bottle is somewhat larger.
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The second sphere experiment was done with the same ball and a nominal 5 ml syringe. The nominal volume of a syringe should be its real volume. I have measured its length and width to make sure and I found that its real volume is about 10% larger. I took that into account in the calculations.
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Icould not provide the accuracy that the subject deserves, but the results aligned better with my V=(√(3.2)r)³ formula.
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I have derived the volume of a cone by comparing a vertical quadrant of a cone to an octant of a sphere.
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<pstyle="margin:12px;">I named my framework the Core Geometric System ™ and put the trademark symbol on it to indicate that this not just another geometric system, this is The Core Geometric System ™.
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It stands for that my logic is built in accordance with the core principles of mathematics. That is something people assume of the conventional one and they have no idea how badly it deviated from that.
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It reflects that my logic is built in accordance with the core principles of mathematics. That is something people assume of the conventional one and they have no idea how badly it deviated from that.
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The expression was unique back then. I came up with it. I never read it anywhere else before. Back then I searched for it to find out if anyone else is using it, and there were no results for that term.
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