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Update index.html
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<img class="center-fit" src="geometry.jpeg" alt="Geometry">
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</div>
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<br>
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<strong style="margin:12px;">This geometric system fundamentally shifts its axioms from the abstract, zero-dimensional point to the square and the cube as the primary, physically-relevant units for measurement.
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<br>
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We define the properties of shapes like the circle and sphere not through abstract limits, but through their direct, rational relationship to these foundational units, resulting in the use of the rational constant 3.2 instead of the irrational pi.
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</strong>
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</p>
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<br>
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<br>
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<p style="margin:12px;"><b>Key Points:</b>
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<br>
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<br>
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<b>- Comparative Geometry:</b> Using geometric relationships to derive areas and volumes.
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<br>
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<br>
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<b>- Scaling and Proportions:</b> Applying proportional relationships for accurate calculations.
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<br>
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<br>
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<b>- Algebraic Manipulation:</b> Simplifying equations to ensure consistency and precision.
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<b>1. Numbers</b>
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<br>
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<br>
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<b>2. Mathematical operations</b>
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<br>
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<b>1. Area of a Circle:</b>
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<br>
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- Compared to a square, using geometric properties and the Pythagorean theorem.
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<b>3. Fractions</b>
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<br>
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- Formula: A = 3.2 × ( square value of the radius ).
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<br>
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<b>4. Powers and numeric systems</b>
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<br>
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<b>2. Circumference of a Circle:</b>
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<br>
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- Derived from the area by subtracting a smaller theoretical circle.
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<b>5. Geometry</b>
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<br>
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- Formula: C = 6.4 × radius.
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<br>
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<br>
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<b>3. Volume of a Sphere:</b>
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<br>
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- Compared to a cube, using the area of the sphere's cross-section.
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<br>
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- Formula: V = " cubic value of ( square root ( 3.2 ) × radius ) ".
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<br>
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<br>
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<b>4. Volume of a Cone:</b>
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<br>
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- Compared to an octant sphere and a quarter cylinder.
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<br>
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- Formula: V = 3.2 × ( square value of the radius ) × height, divided by √8 .
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</p>
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<br>
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<br>
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</div>
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<section>
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<h1 style="font-size:160%;margin:7px">Numbers</h1>
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<br>
@@ -606,7 +577,7 @@ <h2 style="font-size:160%;margin:7px">Mathematical operations</h2>
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<br>
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<br>
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<section>
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<strong style="margin:12px;">"➕ Addition</strong>
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<strong style="margin:12px;">➕ Addition</strong>
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<br>
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<br>
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<p style="margin:12px;">
@@ -663,7 +634,7 @@ <h2 style="font-size:160%;margin:7px">Mathematical operations</h2>
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<br>
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<br>
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<section>
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<strong style="margin:12px;">"➗ Division</strong>
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<strong style="margin:12px;">➗ Division</strong>
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<br>
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<br>
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<p style="margin:12px;">
@@ -686,16 +657,17 @@ <h2 style="font-size:160%;margin:7px">Mathematical operations</h2>
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<br>
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<br>
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<section>
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<h2 style="font-size:160%;margin:7px">Fractions</h2>
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<h3 style="font-size:160%;margin:7px">Fractions</h3>
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<br>
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<br>
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<section>
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<strong style="margin:12px;">"➕ Addition</strong>
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<strong style="margin:12px;">➕ Addition</strong>
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<br>
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<br>
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<p style="margin:12px;">Adding the counters if the denominators are the same.
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<br>
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<br>Example:</p>
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<br>
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Example:</p>
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<br>
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<math style="margin:12px;" xmlns="http://www.w3.org/1998/Math/MathML">
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<mrow>
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<br>
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<p style="margin:12px;">Subtracting the counters if the denominators are the same.
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<br>
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<br>Example:</p>
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<br>
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<math xmlns="http://www.w3.org/1998/Math/MathML">
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Example:</p>
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<br>
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<math p style="margin:12px;" xmlns="http://www.w3.org/1998/Math/MathML">
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<mrow>
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<mfrac><mn>5</mn><mn>3</mn></mfrac>
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<mo>-</mo>
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<mfrac><mn>2</mn><mn>3</mn></mfrac>
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<mo>&#x00D7;</mo>
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<mfrac><mn>4</mn><mn>5</mn></mfrac>
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<mo>=</mo>
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<mfrac>
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<mrow><mo>(</mo><mn>2</mn><mo>&#x00D7;</mo><mn>4</mn><mo>)</mo></mrow>
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<mrow><mo>(</mo><mn>3</mn><mo>&#x00D7;</mo><mn>5</mn><mo>)</mo></mrow>
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<mrow><mo>(</mo><mn>5</mn><mo>-</mo><mn>2</mn><mo>)</mo></mrow>
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<mn>3</mn>
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</mfrac>
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<mo>=</mo>
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<mfrac><mn>8</mn><mn>15</mn></mfrac>
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<mfrac><mn>3</mn><mn>3</mn></mfrac>
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<mo>=</mo>
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<mn>1</mn>
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</mrow>
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</math>
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</math>
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</section>
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<br>
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<br>
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Example:</p>
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<br>
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<math p style="margin:12px;" xmlns="http://www.w3.org/1998/Math/MathML">
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<math xmlns="http://www.w3.org/1998/Math/MathML">
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<mrow>
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<mfrac><mn>5</mn><mn>3</mn></mfrac>
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<mo>-</mo>
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<mfrac><mn>2</mn><mn>3</mn></mfrac>
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<mo>&#x00D7;</mo>
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<mfrac><mn>4</mn><mn>5</mn></mfrac>
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<mo>=</mo>
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<mfrac>
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<mrow><mo>(</mo><mn>5</mn><mo>-</mo><mn>2</mn><mo>)</mo></mrow>
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<mn>3</mn>
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<mrow><mo>(</mo><mn>2</mn><mo>&#x00D7;</mo><mn>4</mn><mo>)</mo></mrow>
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<mrow><mo>(</mo><mn>3</mn><mo>&#x00D7;</mo><mn>5</mn><mo>)</mo></mrow>
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</mfrac>
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<mo>=</mo>
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<mfrac><mn>3</mn><mn>3</mn></mfrac>
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<mo>=</mo>
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<mn>1</mn>
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<mfrac><mn>8</mn><mn>15</mn></mfrac>
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</mrow>
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</math>
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</section>
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<br>
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<br>
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<section>
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<strong style="margin:12px;">"➗ Division</strong>
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<strong style="margin:12px;">➗ Division</strong>
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<br>
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<br>
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<p style="margin:12px;">Dividing by a fraction equals multiplying by its reciprocal.</p>
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<br>
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<br>
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<br>
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Example:</p>
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<br>
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<section>
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<h3 style="font-size:160%;margin:7px">Powers, numeral systems and basic geometry</h1>
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<h4 style="font-size:160%;margin:7px">Powers, numeral systems and basic geometry</h4>
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<br>
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<br>
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<section>
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<p style="margin:12px;"><strong>Powers</strong>
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<br>
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<br>
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Example #3: 4^(1/2) = √4 = 2
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</p>
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</section>
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<br>
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<section>
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</section>
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<br>
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<br>
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<div>
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<section>
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<p style="font-size:160%;font-weight:bold;margin:7px">Trigonometry</p>
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<br>
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<div class="imgbox">
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</mrow>
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</math>
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</div>
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</section>
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<br>
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<br>
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<br>
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<section><strong>This geometric system fundamentally shifts its axioms from the abstract, zero-dimensional point to the square and the cube as the primary, physically-relevant units for measurement.
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<br>
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We define the properties of shapes like the circle and sphere not through abstract limits, but through their direct, rational relationship to these foundational units, resulting in the use of the rational constant 3.2 instead of the irrational pi.
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</strong>
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<br>
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<br>
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<p style="margin:12px;"><b>Key Points:</b>
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<br>
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<br>
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<b>- Comparative Geometry:</b> Using geometric relationships to derive areas and volumes.
1956+
<br>
1957+
<br>
1958+
<b>- Scaling and Proportions:</b> Applying proportional relationships for accurate calculations.
1959+
<br>
1960+
<br>
1961+
<b>- Algebraic Manipulation:</b> Simplifying equations to ensure consistency and precision.
1962+
<br>
1963+
<br>
1964+
<br>
1965+
<b>1. Area of a Circle:</b>
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<br>
1967+
- Compared to a square, using geometric properties and the Pythagorean theorem.
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<br>
1969+
- Formula: A = 3.2 × ( square value of the radius ).
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<br>
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<br>
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<b>2. Circumference of a Circle:</b>
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<br>
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- Derived from the area by subtracting a smaller theoretical circle.
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<br>
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- Formula: C = 6.4 × radius.
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<br>
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<br>
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<b>3. Volume of a Sphere:</b>
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<br>
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- Compared to a cube, using the area of the sphere's cross-section.
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<br>
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- Formula: V = " cubic value of ( square root ( 3.2 ) × radius ) ".
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<br>
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<br>
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<b>4. Volume of a Cone:</b>
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<br>
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- Compared to an octant sphere and a quarter cylinder.
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<br>
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- Formula: V = 3.2 × ( square value of the radius ) × height, divided by √8 .
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</p>
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<br>
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<br>
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<br>
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<br>
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</section>
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<div>
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<strong style="font-size:160%;margin:7px">Area of a circle</strong>
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<br>
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<br>
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<div>
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<p style="margin:12px;">/ 🚧 Experimental section under construction 🚧 /</p>
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<br>
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<br>
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<div>
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<p style="margin:12px;"><strong>"h1-a"Numbers</strong></p>
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<div>
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<p style="margin:12px;">Example #2 - The year 2025 in Roman numbers</p>
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<table border="1" cellpadding="8" cellspacing="0">
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<thead>
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<tr>
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<th>Values</th>
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<th> </th>
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<th>1</th>
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<th>2</th>
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<th>3</th>
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<th>4</th>
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<th>5</th>
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<th>6</th>
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<th>7</th>
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<th>8</th>
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<th>9</th>
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<th>10</th>
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<th>50</th>
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<th>100</th>
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<th>500</th>
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<br>
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<br>
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<br>
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<br>
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<div>
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<p style="margin:12px;"><strong>"h2"operations</strong></p>
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<br>
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<br>
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</div>
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<br>
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<br>
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<footer>
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<p style="margin:12px;">® All rights reserved</p>
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<br>

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