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@@ -305,21 +305,18 @@ <h1 style="font-size:160%;margin:7px;">About the Core Geometric System ™</h1>
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That got me excited for obvious reasons, but also confused. Nobody thought of that before? Why is the π so different?
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For a long time I just kept thinking and calculating all aspects of that, and I just shared my finding with friends about a year later. But they didn't share my excitement.
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For a long time I just kept thinking and calculating all aspects of that, and I just shared my finding with a few friends. About a year later I concluded that they didn't share my excitement.
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Some of them didn't really care about math at all, those who did were sticking to the π, just because it's an old and highly hyped convention.
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</p>
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</section>
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<section><pstyle="margin:12px;">
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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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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.
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These included a ping-pong ball, a golf ball and a vodka bottle that I found somewhere.
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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 better with my V = ( √( 3.2 )r)³ formula than the conventional "4 / 3 × π × r³". It's quite hard to physically measure the volume of a ball accurately, but there's a significant difference between the results of the two formulas that was easy to see.
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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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</section>
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<section><pstyle="margin:12px;">In 2020 there were news about that online education will be introduced because of the pandemic.
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<section><pstyle="margin:12px;">In early 2020 there were news about that online education will be introduced because of the pandemic.
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I thought my discoveries can be useful for others, too, so I shared them online.
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I thought my discoveries can be useful for others, too, so I went to the loal public library to share them online as a webpage.
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That was another challenge because I didn't have a routine in that either.
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That was another challenge because I didn't have a routine in web development either.
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Under some sorts of different pressures I made all kinds of mistakes. My volume formula for a cone and a pyramid was undeveloped and I wasn't totally comfortable with my content overall but I had to start somewhere.
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My attention was divided by all the details in both geometry and IT.
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My attention was divided by lots of details in both geometry and IT.
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I got 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 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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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 1st principles, what should I prove about those?
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Also I didn't see how the so-called "proofs" of the conventional formulas prove anything. They are nonsensical and exaggerated. Only I see that?
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Also I didn't see how the so-called "proofs" of the conventional formulas prove anything. They are superficial and some of them are even exaggerated and nonsensical. Only I see that?
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Then I realized that it is about something else. It's the old "We have a diploma, so we are right." thing.
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That is something to think about for a moment.
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Years have passed without much happening. I solved geometry puzzles on social media. I developed some routine and learned a lot. And I slowly realized bit by bit that through my formulas I have created a logically interconnected, consistent geometric framework.
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Years have passed without significant development. I was working on improving my online presence and solved geometry puzzles on social media. You can find my favorites on X in the replies of @BasicGeometry. Solving puzzles is fun, and helps to learn and develop some routine.
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Bit by bit I slowly realized that through my formulas I have created a logically interconnected, consistent geometric framework.
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Something that the common man would assume of the conventional one. There are several geometry concepts, but there's a popular one that they teach in schools and online.
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Something that the one would assume of the conventional geometry. There are several geometry concepts, but there's a popular one that they teach in schools and online.
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That starts with that "a point is a zero-dimensional entity", "the line has no thickness" and states that "the ratio between the circumference and the diameter of a circle is π", "the volume of a sphere is 4 / 3 × π × r³", "the volume of a cone and a pyramid is base × height / 3", and all that is "rigorously proven via calculus".
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They call that Euclidean geometry.
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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 the key difference is 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 when in case of 3 dimensional solids.
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Deriving 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.
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</p>
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</section>
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<section><pstyle="margin:12px;">In 2024 I got access to AI language models.
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<iframetitle="Introduction to basic geometry" width="420" height="315" src="https://youtube.com/embed/U5eHkmmVVEA">
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</iframe>
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</div>
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</section>
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That got things going. One generated me great figures, another one helped to develop the proof for my circle area formula, and they helped me to disapprove the conventional ones by summarizing the key points of conventional geometry.
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It wasn't a cakewalk though, because they acted just like the academic wise guys protecting their diplomas. They kept calling the conventional stuff well-established and rigorously proven, and mine as a deviation.
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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 was very annoying. But they are programmed to answer my questions. And I questioned them until they revealed all the inconsistent details they were trying to hide.
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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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Those are the logical flaws in conventional geometry.
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Interestingly, now language models explain it like some general term without even referencing my work.
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<section>
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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 any core geometric system, this is *the* Core Geometric System ™.
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<section><pstyle="margin:12px;">In 2024 I fixed the numeric value for my cone and pyramid volume formula. I'm sorry about having presented a wrong number for such a long time, but at least my logic was closer to reality.
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The term itself 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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Interestingly, now language models explain it like some general term.
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Later that year I got access to AI language models.
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Unlike others, my framework relies on 1st principles and it's logically consistent.
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That got things going. One generated me great figures, another one helped to develop the proof for my circle area formula, and they helped me to get my phrasing and the technical part of my website in shape.
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It's quite similar to the Euclidean, but the key difference is that a point is not zero-dimensional and a line can have a thickness. These two make a big difference, especially in 3 dimensional solids
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They also helped to disapprove the conventional formulas by summarizing their key points.
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The rest is about deriving the properties of different shapes, which is not really about if it is Euclidean or not, but since Archimedes' flawed formulas are associated with it, I figured that it's the best to start with a clear sheet.
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It wasn't a cakewalk though, because they acted just like the academic wise guys protecting their diplomas. They kept calling the conventional stuff well-established and rigorously proven, and mine as a deviation.
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It was very disturbing. But I was able to catch their recurring arguments. And I questioned them until they revealed all the inconsistent details they were trying to hide.
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That is the Core Geometric System ™. What geometry was originally meant to be before it was derailed by Archimedes.
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Those are the logical flaws in conventional geometry.
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<iframetitle="Introduction to basic geometry" width="420" height="315" src="https://youtube.com/embed/U5eHkmmVVEA">
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