You signed in with another tab or window. Reload to refresh your session.You signed out in another tab or window. Reload to refresh your session.You switched accounts on another tab or window. Reload to refresh your session.Dismiss alert
<h2>Once around 2018 I was wondering how to calculate the area of a circle.</h2>
115
119
<section>
116
-
<h2itemprop="disambiguatingDescription">I remembered the number 3.14 called the pi, 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.</h2>
120
+
<h2>I remembered the number 3.14 called the pi, 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.</h2>
117
121
<br>
118
-
<pitemprop="text">The only problem with that was that the circle is not square. I have figured that the circle can be cut in four and then I get four right angles that can be aligned with the vertices of a square.
122
+
<p>The only problem with that was that the circle is not square. I have figured that the circle can be cut in four and then I get four right angles that can be aligned with the vertices of a square.
119
123
<br>
120
124
There was a different problem with that: The quadrant circles overlap at some places but the middle of the square is uncovered.
121
125
<br>
@@ -138,17 +142,17 @@ <h2 itemprop="disambiguatingDescription">I remembered the number 3.14 called the
138
142
</iframe>
139
143
</div>
140
144
<br>
141
-
<pitemprop="text">That got me excited for obvious reasons, but also confused. Nobody thought of that before? Why is the pi so different?
145
+
<p>That got me excited for obvious reasons, but also confused. Nobody thought of that before? Why is the pi so different?
142
146
<br>
143
147
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.
144
148
<br>
145
149
Some of them didn't really care about math at all, those who did were sticking to the pi, just because it's an old and highly hyped convention.</p>
146
150
</section>
147
151
<br><br><br>
148
152
<section>
149
-
<h2itemprop="description">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>
153
+
<h2>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>
150
154
<br>
151
-
<pitemprop="text">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 ".
155
+
<p>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 ".
152
156
<br><br>
153
157
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.</p>
154
158
<br>
@@ -157,7 +161,7 @@ <h2 itemprop="description">Meanwhile I figured that by extending the area of a c
157
161
</iframe>
158
162
</div>
159
163
<br>
160
-
<pitemprop="text">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.
164
+
<p>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.
161
165
<br>
162
166
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.</p>
163
167
<br>
@@ -166,19 +170,19 @@ <h2 itemprop="description">Meanwhile I figured that by extending the area of a c
166
170
</iframe>
167
171
</div>
168
172
<br>
169
-
<pitemprop="text">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.</p>
173
+
<p>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.</p>
170
174
</section>
171
175
<br><br><br>
172
176
<section>
173
-
<h2itemprop="description">I have derived the volume of a cone by comparing a vertical quadrant of a cone to an octant of a sphere.</h2>
177
+
<h2>I have derived the volume of a cone by comparing a vertical quadrant of a cone to an octant of a sphere.</h2>
174
178
<br>
175
-
<pitemprop="text">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>
179
+
<p>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>
176
180
</section>
177
181
<br><br><br>
178
182
<section>
179
-
<h2itemprop="description">In early 2020 there were news about that online education was introduced because of the pandemic.</h2>
183
+
<h2>In early 2020 there were news about that online education was introduced because of the pandemic.</h2>
180
184
<br>
181
-
<pitemprop="text">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.
185
+
<p>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.
182
186
<br><br>
183
187
I received some criticism regarding my formulas. Those included the lack of rigorous proof, and the alleged rigorous proofs of the conventional formulas.
184
188
<br>
@@ -194,7 +198,7 @@ <h2 itemprop="description">In early 2020 there were news about that online educa
194
198
<br><br>
195
199
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.</p>
196
200
<br>
197
-
<pitemprop="disambiguatingDescription">Eventually I have realized that through my formulas I have created a logically interconnected, consistent geometric framework.
201
+
<p>Eventually I have realized that through my formulas I have created a logically interconnected, consistent geometric framework.
198
202
<br>
199
203
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.
200
204
<br>
@@ -210,13 +214,13 @@ <h2 itemprop="description">In early 2020 there were news about that online educa
210
214
<iframetitle="Introduction to basic geometry" width="420" height="315" src="https://youtube.com/embed/U5eHkmmVVEA"></iframe>
211
215
</div>
212
216
<br>
213
-
<pitemprop="description">Exactly determining the properties of different shapes is in the scope.</p>
217
+
<p>Exactly determining the properties of different shapes is in the scope.</p>
214
218
</section>
215
219
<br><br><br>
216
220
<section>
217
-
<h2itemprop="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>
221
+
<h2>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>
218
222
<br>
219
-
<pitemprop="text">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.
223
+
<p>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.
220
224
<br><br>
221
225
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.
222
226
<br>
@@ -226,9 +230,9 @@ <h2 itemprop="description">I named my framework the Core Geometric System ™ an
226
230
</section>
227
231
<br><br><br>
228
232
<section>
229
-
<h2itemprop="description">In 2024 I fixed the numeric value for my cone and pyramid volume formula. </h2>
233
+
<h2>In 2024 I fixed the numeric value for my cone and pyramid volume formula. </h2>
230
234
<br>
231
-
<pitemprop="text">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.
235
+
<p>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.
232
236
<br><br>
233
237
Later that year I got access to AI language models.
234
238
<br>
@@ -244,9 +248,9 @@ <h2 itemprop="description">In 2024 I fixed the numeric value for my cone and pyr
244
248
</section>
245
249
<br><br><br>
246
250
<section>
247
-
<h2itemprop="description">While trying to explain it to others, I have found that different people have different levels of education.</h2>
251
+
<h2>While trying to explain it to others, I have found that different people have different levels of education.</h2>
248
252
<br>
249
-
<pitemprop="text">I thought I can't just start the explanation with the numbers and basic operations.
253
+
<p>I thought I can't just start the explanation with the numbers and basic operations.
250
254
<br>
251
255
Then I realized that I can.
252
256
<br>
@@ -266,14 +270,16 @@ <h2 itemprop="description">While trying to explain it to others, I have found th
0 commit comments