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"description": "Real physical experiment to measure the volume of a sphere using liquid displacement and a certified bottle. The result proves the accuracy of the V=(√(3.2)r)³ formula over the conventional V=4/3 × pi × r³.",
"description": "Real physical experiment to measure the volume of a sphere using liquid displacement and a syringe. The result proves the accuracy of the V=(√(3.2)r)³ formula over the conventional V=4/3 × pi × r³.",
"usageInfo": "Discover the Core Geometric System ™, a groundbreaking framework offering a fresh perspective on calculating area and volume using the 3D coordinate system. Introducing exact, empirically grounded and logically consistent formulas instead of the flawed conventional approximations."
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<h1style="font-size:160%;margin:7px">About the Core Geometric System ™</h1>
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<h2style="margin:12px">Once around 2018 I was wondering how to calculate the area of a circle.</h2>
<h2itemprop="about" style="margin:12px">Once around 2018 I was wondering how to calculate the area of a circle.</h2>
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<section><h2style="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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<pstyle="margin:12px">Because the square is the basis of area calculation. That is why we use square units.
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<sectionitemscopeitemtype="http://schema.org/articleSection"><h2style="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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<pitemrel="description" style="margin:12px">Because the square is the basis of area calculation. That is why we use square units.
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The only problem with that was that the circle is not square. I have figured that the circle can be cut into four and then I get four right angles that can be aligned with the vertices of a square.
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Then I worked out the relationship between the radius and the side of the square algebraically via the Pythagorean theorem.
The result is that the area of a circle is exactly 3.2radius².
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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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<pstyle="margin:12px" itemrel="description">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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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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<pstyle="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 ".
<h2style="margin:12px" itemrel="about">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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<pitemrel="description" 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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With the limited resources that I had, I conducted some experiments.
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I conducted some experiments with the resources that I had.
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 ~ 4 / 3 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. 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.
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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<pstyle="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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<pstyle="margin:12px" itemrel="description">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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<h2style="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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<pstyle="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.
<h2itemrel="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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<pitemrel="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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<h2style="margin:12px">In early 2020 there were news about that online education was introduced because of the pandemic.</h2>
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<pstyle="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.
<h2itemprop="about" style="margin:12px">In early 2020 there were news about that online education was introduced because of the pandemic.</h2>
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<pitemrel="description" 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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I received some negative criticism regarding my formulas. Those included the lack of rigorous proof, and the alleged rigorous proofs of the conventional formulas.
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I received some criticism regarding my formulas. Those included the lack of rigorous proof, and the alleged rigorous proofs of the conventional formulas.
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Obviously I wasn't happy about those, but I felt like there's not much I can do about that. I derived my formulas from first principles, what should I prove about those?
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<iframetitle="Introduction to basic geometry" width="420" height="315" src="https://youtube.com/embed/U5eHkmmVVEA">
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<h2style="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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<pstyle="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.
<h2itemrel="about" 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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<pitemrel="description" 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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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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<h2style="margin:12px">In 2024 I fixed the numeric value for my cone and pyramid volume formula. </h2>
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<pstyle="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.
<h2itemprop="about" style="margin:12px">In 2024 I fixed the numeric value for my cone and pyramid volume formula. </h2>
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<pitemrel="description" 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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Later that year I got access to AI language models.
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<h2style="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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<pstyle="margin:12px">I thought I can't just start the explanation with the numbers and basic operations.
<h2itemprop="about" 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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<pitemrel="description" 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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