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@@ -507,52 +507,53 @@ <h2 style="font-size:100%">By fundamentally shifting the axioms from the abstrac
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<h3>Key Points</h3>
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<h3 style="margin:7px;">Key Points</h3>
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<br>
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<br>
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<h4>Comparative Geometry</h4>
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<p style="margin:12px;">Using geometric relationships to derive areas and volumes.
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</p>
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<br>
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<h4>Scaling and Proportions</h4>
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<p style="margin:12px;">Applying proportional relationships for accurate calculations.
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</p>
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<br>
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<h4>Algebraic Manipulation</h4>
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<p style="margin:12px;">Simplifying equations to ensure consistency and precision.
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</p>
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<br>
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<h5>1. Area of a Circle</h5>
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<h4 style="margin:7px;">1. Area of a Circle</h5>
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<br>
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<p style="margin:12px;">Compared to a square, using geometric properties and the Pythagorean theorem.
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<br>
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Formula: A = 3.2 × ( square value of the radius ).
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</p>
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<br>
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<h5>Circumference of a Circle</h5>
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<h4 style="margin:7px;">2. Circumference of a Circle</h5>
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<br>
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<p style="margin:12px;">Derived from the area by subtracting a smaller theoretical circle.
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Formula: C = 6.4 × radius.
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</p>
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<br>
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<h5>Volume of a Sphere</h5>
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<h5 style="margin:7px;">3. Volume of a Sphere</h5>
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<br>
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<p style="margin:12px;">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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</p>
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<br>
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<h5>Volume of a Cone</h5>
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<h5 style="margin:7px;">4. Volume of a Cone</h5>
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<br>
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<p style="margin:12px;">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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<h5 style="margin:7px;">Comparative Geometry</h4>
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<p style="margin:12px;">Using geometric relationships to derive areas and volumes.
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</p>
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<br>
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<h5 style="margin:7px;">Scaling and Proportions</h4>
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<p style="margin:12px;">Applying proportional relationships for accurate calculations.
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</p>
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<br>
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<h5 style="margin:7px;">Algebraic Manipulation</h4>
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<p style="margin:12px;">Simplifying equations to ensure consistency and precision.
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</p>
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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>
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<h2 style="margin:7px;">The Basic Geometry Curriculum</h2>
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<br>
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<h3>Modules:</h3>
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<h3 style="margin:7px;">Modules:</h3>
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<section>
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<details>
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<summary><h3>1. Numbers and numeric systems</h3></summary>
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<summary><h3 style="margin:7px;">1. Numbers and numeric systems</h3></summary>
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<section><h4>Numbers</h4>
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<section><h4 style="margin:12px;">Numbers</h4>
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<table>
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<thead>
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<section>
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<h4>Numeric systems</h4>
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<h4 style="margin:12px;">Numeric systems</h4>
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Example #1 - The year 2025 in the decimal system with Arab numerals</p>
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<section>
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<details>
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<summary><h3>2. Mathematical operations</h3></summary>
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<summary><h3 style="margin:7px;">2. Mathematical operations</h3></summary>
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<section>
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<h4>= The equity symbol</h4>
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<h4 style="margin:12px;">= The equity symbol</h4>
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<br>
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<p style="margin:12px;">The numbers or expressions of one side equal in value to the other side.
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<section>
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<h4>➕ Addition</h4>
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<h4 style="margin:12px;">➕ Addition</h4>
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<p style="margin:12px;">Example #1:
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<section>
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<h4>➖ Subtraction</h4>
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<h4 style="margin:12px;">➖ Subtraction</h4>
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<p style="margin:12px;">The opposite of addition
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<section>
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<h4>✖️ Multiplication</h4>
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<h4 style="margin:12px;">✖️ Multiplication</h4>
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<p style="margin:12px;">An advanced form of addition
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<section>
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<h4>➗ Division</h4>
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<h4 style="margin:12px;">➗ Division</h4>
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<p style="margin:12px;">An advanced from of subtraction, the logical opposite of multiplication
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<section>
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<summary><h3>3. Fractions</h3></summary>
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<summary><h3 style="margin:7px;">3. Fractions</h3></summary>
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<p style="margin:12px;">Fractions are results of division, some are non-whole numbers.
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<p style="margin:12px;"><h3>Operations with fractions</h3>
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<p style="margin:12px;"><h3 style="margin:7px;">Operations with fractions</h3>
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<h4>➕ Adding fractions</h4>
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<h4 style="margin:12px;">➕ Adding fractions</h4>
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<p style="margin:12px;">Adding the counters if the denominators are the same.
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<h4>➖ Subtracting fractions</h4>
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<h4 style="margin:12px;">➖ Subtracting fractions</h4>
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<p style="margin:12px;">Subtracting the counters if the denominators are the same.
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<h4>✖️ Multiplying fractions</h4>
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<h4 style="margin:12px;">✖️ Multiplying fractions</h4>
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<p style="margin:12px;">Multiplying counter by counter and denominator by denominator.
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<section>
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<h4>➗ Dividing fractions</h4>
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<h4 style="margin:12px;">➗ Dividing fractions</h4>
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<p style="margin:12px;">Dividing by a fraction equals multiplying by its reciprocal.
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<summary><h3>4. Powers</h3></summary>
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<summary><h3 style="margin:7px;">4. Powers</h3></summary>
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<p style="margin:12px;">Raising a number or unit of measurement to a power means multiplying it by itself.

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