Update about.html

Text formatting

Author: Gmac4247

about.html

@@ -204,7 +204,7 @@
 "@type": "AdministrativeArea",
 "name" :"Szentendre, Hungary"
 	},
-"schemaVersion": "https://schema.org/docs/releases.html#v29.2",
+"schemaVersion": "https://schema.org/docs/releases.html#v29.3",
 "sdDatePublished": "2024-08-31",
 "sdPublisher": {
 "@type": "Person" ,
@@ -286,26 +286,20 @@ <h1 style="font-size:160%;margin:7px;">About the Core Geometric System ™</h1>
 I remembered the number 3.14 called the π, but I was interested in the logic of comparing the circle to a square. 
 Because the square is the basis of area calculation. That is why we use square units. 
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-<br>
 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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-<br>
 There was a different problem with that: The quadrant circles overlap at some places but the middle of the square is uncovered.
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-<br>
 I was trying to match the overlapping area with the uncovered by eye. 
 When it looked quite close I did all kinds of complicated calculations. 
 I didn't have a routine in that and I wanted to calculate all aspects of it. 
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 I calculated quite intensively and my calculations were quite extensive. When a backcheck resulted in an error I felt quite tired of it and just layed the figure face down.
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-<br>
 About a month later I had a look at it and I realized at the first glimpse that the area of the circle equals the area of the square when the arcs of the qudrant circles intersect at the quarters of the centerlines.
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 Maybe that doesn't sound very scientific at first, but somehow I instantly realized that it is the only way.
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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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@@ -328,48 +322,52 @@ <h1 style="font-size:160%;margin:7px;">About the Core Geometric System ™</h1>
 </section>
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-<section><p style="margin:12px;">
+<section>
+<p style="margin:12px;">
 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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 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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 With the limited resources that I had, I conducted some experiments.
-<br>
+</p>
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 <div>
  <iframe title="The sphere experiment" width="420" height="315" src="https://youtube.com/embed/7uxyLfh2B38">
  </iframe>
 </div>
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+<p style="margin:12px;">
 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.
-<br>
+</p>
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 <div>
  <iframe title="The sphere experiment 2" width="420" height="315" src="https://youtube.com/embed/rXcJhFLLP0Y">
  </iframe>
 </div>
-<br>
+<p style="margin:12px;">
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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.
+</p>
+</section>
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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.
-<br>
-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. 
+<section>
+<p 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.
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+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.
 </p>
 </section>
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-<section><p style="margin:12px;">In early 2020 there were news about that online education will be introduced because of the pandemic. I thought it was time to share my discoveries online, so I went to the loal public library to publish them on a webpage. 
+<section>
+<p style="margin:12px;">In early 2020 there were news about that online education will be introduced because of the pandemic. I thought it was time to share my discoveries online, so I went to the loal public library to publish them on a webpage. 
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 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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@@ -390,15 +388,16 @@ <h1 style="font-size:160%;margin:7px;">About the Core Geometric System ™</h1>
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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. 
+<br>
+Eventually I have realized that through my formulas I have created a logically interconnected, consistent geometric framework. 
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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. 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 when in case of 3 dimensional solids. 
+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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 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.