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@@ -96,7 +96,7 @@ <h1 style="font-size:160%;margin:7px">About the Core Geometric System ™</h1>
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<article itemscope itemtype="http://schema.org/Article">
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<h2 itemprop="about" style="margin:12px">Once around 2018 I was wondering how to calculate the area of a circle.</h2>
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<h2 itemrel="description" style="margin:12px">Once around 2018 I was wondering how to calculate the area of a circle.</h2>
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<section><h2 itemrel="description" style="margin:12px">I remembered the number 3.14 called the pi, but I was interested in the logic of comparing the circle to a square.</h2>
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<p style="margin:12px">Because the square is the basis of area calculation. That is why we use square units.
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Then I worked out the relationship between the radius and the side of the square algebraically via the Pythagorean theorem.
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<iframe title="Geometry puzzle" width="420" height="315" src="https://youtube.com/embed/-gvXLaLFXuM">
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<p style="margin:12px">That got me excited for obvious reasons, but also confused. Nobody thought of that before? Why is the pi so different?
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For about a year I just kept thinking and calculating all aspects of that, and I shared my discovery just with a few friends. They didn't share my excitement.
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<h2 style="margin:12px">Meanwhile I figured that by extending the area of a circle to 3D, the volume of a sphere equals the cubed value of the square root of its cross-sectional area, just like a cube.</h2>
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<h2 itemrel="description" style="margin:12px">Meanwhile I figured that by extending the area of a circle to 3D, the volume of a sphere equals the cubed value of the square root of its cross-sectional area, just like a cube.</h2>
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<p style="margin:12px">It's quite hard to physically accurately measure the volume of a ball, but there's a significant difference between the result of my V=(√(3.2)r)³ formula and the conventional " 4 / 3 × pi × r³ ".
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I conducted some experiments with the resources that I had. I could 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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<iframe title="The sphere experiment" width="420" height="315" src="https://youtube.com/embed/7uxyLfh2B38">
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<iframe title="The sphere experiment 2" width="420" height="315" src="https://youtube.com/embed/rXcJhFLLP0Y">
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<p style="margin:12px" itemrel="description">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. However, 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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<h2 itemrel="about" style="margin:12px">I have derived the volume of a cone by comparing a vertical quadrant of a cone to an octant of a sphere.</h2>
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<p itemrel="description" style="margin:12px">First I made a mistake in that. I knew that the height has to be divided by 2, not 3 as they usually do it, but I confused the vertical height with the slant height and I divided it by 2 only once, instead of twice. That resulted in an error.
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<h2 itemrel="description" style="margin:12px">I have derived the volume of a cone by comparing a vertical quadrant of a cone to an octant of a sphere.</h2>
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<p style="margin:12px">First I made a mistake in that. I knew that the height has to be divided by 2, not 3 as they usually do it, but I confused the vertical height with the slant height and I divided it by 2 only once, instead of twice. That resulted in an error.
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<h2 style="margin:12px">In early 2020 there were news about that online education was introduced because of the pandemic.</h2>
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<h2 itemrel="description" style="margin:12px">In early 2020 there were news about that online education was introduced because of the pandemic.</h2>
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<p style="margin:12px">I thought it was time to share my discoveries online, so I went to the local public library to publish them on a webpage. My volume formula for a cone and a pyramid was undeveloped and I didn't have much web development skills but I had to start somewhere. My attention was divided by lots of details in both geometry and IT.
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They call that Euclidean geometry. I primarily regard my framework as a fix of the conventional one.
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It's quite similar to the Euclidean, but apparently the key differences are that I don't define the point is as zero-dimensional and a line can have a thickness. These two make a big difference, especially in case of 3 dimensional solids.
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Since conventional geometry is associated with the zero-dimensional point and Archimedes' flawed formulas, I figured that it's the best to start with a clear sheet.</p>
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<iframe title="Introduction to basic geometry" width="420" height="315" src="https://youtube.com/embed/U5eHkmmVVEA">
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<p itemrel="description" style="margin:12px">Exactly determining the properties of different shapes is in the scope, which is not really about if it is Euclidean or not. But since that is associated with the zero-dimensional point and Archimedes' flawed formulas, I figured that it's the best to start with a clear sheet.</p>
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<p itemrel="description" style="margin:12px">Exactly determining the properties of different shapes is in the scope.</div>
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<h2 style="margin:12px">I named my framework the Core Geometric System ™ and put the trademark symbol on it to indicate that this not just another abstract geometric system.</h2>
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<h2 style="margin:12px" itemrel="description">I named my framework the Core Geometric System ™ and put the trademark symbol on it to indicate that this not just another abstract geometric system.</h2>
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<p style="margin:12px">The name reflects that my logic is built in accordance with the core principles of elementary mathematics. That is something that people assume of the conventional one and they have no idea how badly it deviated from that.
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<h2 style="margin:12px">In 2024 I fixed the numeric value for my cone and pyramid volume formula. </h2>
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<h2 style="margin:12px" itemrel="description">In 2024 I fixed the numeric value for my cone and pyramid volume formula. </h2>
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<p style="margin:12px">I'm sorry about that I had presented a wrong number for such a long time, but at least my logic was closer to reality.
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<h2 style="margin:12px">While trying to explain it to others, I have found that different people have different levels of education.</h2>
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<h2 style="margin:12px" itemrel="description">While trying to explain it to others, I have found that different people have different levels of education.</h2>
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<p style="margin:12px">I thought I can't just start the explanation with the numbers and basic operations.
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Then I realized that I can.

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