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Enhance text emphasis with strong tags
Added strong emphasis to various sections for clarity. Added rounded button style.
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index.html

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@@ -68,7 +68,18 @@
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#cookie-notice-buttons button:hover {
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background-color: #3e8e41;
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}
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.rounded-button {
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display: inline-block;
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padding: 10px 20px;
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background-color: #007bff;
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color: white;
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text-decoration: none;
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border-radius: 15px;
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text-align: center;
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transition: background-color 0.3s ease;
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}
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body {
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font-family: 'OpenDyslexic', sans-serif;
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}
@@ -511,48 +522,54 @@ <h3 style="margin:7px;">Key Points</h3>
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<br>
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<a style="margin:7px;" href="#circle">Area of a Circle</a>
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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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<strong style="margin:12px;">Compared to a square, using geometric properties and the Pythagorean theorem.
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<br>
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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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</strong>
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<br>
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<br>
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<a style="margin:7px;" href="#circumference">Circumference of a Circle</a>
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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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<strong style="margin:12px;">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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</p>
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</strong>
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<br>
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<br>
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<a style="margin:7px;" href="#sphere">Volume of a Sphere</a>
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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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<strong 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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<br>
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Formula: V = cubic value of ( square root ( 3.2 ) × radius )
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</p>
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</strong>
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<br>
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<br>
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<a style="margin:7px;" href="#cone">Volume of a Cone</a>
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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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<strong style="margin:12px;">Compared to an octant sphere and a quarter cylinder.
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<br>
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<br>
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Formula: V = 3.2 × ( square value of the radius ) × height, divided by square root ( 8 )
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</p>
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</strong>
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<br>
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<br>
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<h4 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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<strong style="margin:12px;">Using geometric relationships to derive areas and volumes.
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</strong>
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<br>
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<h4 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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<strong style="margin:12px;">Applying proportional relationships for accurate calculations.
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</strong>
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<br>
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<h4 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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<strong style="margin:12px;">Simplifying equations to ensure consistency and precision.
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</strong>
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</section>
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<br>
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<br>
@@ -3165,7 +3182,7 @@ <h4 style="margin:12px;">Archimedes and the Polygonal Trap</h4>
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What we’re left with is not a proof, but a layered approximation — one that has shaped centuries of geometry, but now deserves a closer, more rational reexamination.
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<strong>Similarly, the area formula A = πr² is not a direct result of calculus. It’s reverse-engineered by multiplying the circumference formula C = 2πr by half the radius—treating the area as the sum of infinitesimal rings.</strong> While the result of that method is algebraically valid, it bypasses the geometric logic that defines area: the comparison to a square.
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<strong>Similarly, the area formula A = πr² is not a direct result of calculus. It’s reverse-engineered by multiplying the circumference formula C = 2πr by half the radius—treating the area as the sum of infinitesimal rings. While the result of that method is algebraically valid, it bypasses the geometric logic that defines area: the comparison to a square.</strong>
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</p>
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</section>
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<br>
@@ -3296,10 +3313,11 @@ <h4 style="margin:12px;">A Rational Alternative: 3.2</h4>
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These values are exact, rational, and logically derived. They can be verified numerically, but more importantly, they can be proven algebraically—without relying on infinite fractions, symbolic shortcuts, or flawed assumptions.
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Since the true ratio is exactly 3.2, and that is a rational number, then we can—and should—write it as it is. Let the π remain in the history books. Geometry deserves better.
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<strong>Since the true ratio is exactly 3.2, and that is a rational number, then we can—and should—write it as it is. Let the π remain in the history books. Geometry deserves better.
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That makes the arc value of 360° = 6.4radian, and trigonometric functions that rely on arc value have to be aligned to 3.2 respectively.
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</strong>
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These are two aspects of that.

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