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68 | 68 | #cookie-notice-buttons button:hover { |
69 | 69 | background-color: #3e8e41; |
70 | 70 | } |
71 | | - |
| 71 | + |
| 72 | + .rounded-button { |
| 73 | + display: inline-block; |
| 74 | + padding: 10px 20px; |
| 75 | + background-color: #007bff; |
| 76 | + color: white; |
| 77 | + text-decoration: none; |
| 78 | + border-radius: 15px; |
| 79 | + text-align: center; |
| 80 | + transition: background-color 0.3s ease; |
| 81 | + } |
| 82 | + |
72 | 83 | body { |
73 | 84 | font-family: 'OpenDyslexic', sans-serif; |
74 | 85 | } |
@@ -511,48 +522,54 @@ <h3 style="margin:7px;">Key Points</h3> |
511 | 522 | <br> |
512 | 523 | <a style="margin:7px;" href="#circle">Area of a Circle</a> |
513 | 524 | <br> |
514 | | -<p style="margin:12px;">Compared to a square, using geometric properties and the Pythagorean theorem. |
| 525 | +<strong style="margin:12px;">Compared to a square, using geometric properties and the Pythagorean theorem. |
515 | 526 | <br> |
516 | 527 | <br> |
517 | 528 | Formula: A = 3.2 × ( square value of the radius ) |
518 | | -</p> |
| 529 | +</strong> |
| 530 | +<br> |
519 | 531 | <br> |
520 | 532 | <a style="margin:7px;" href="#circumference">Circumference of a Circle</a> |
521 | 533 | <br> |
522 | | -<p style="margin:12px;">Derived from the area by subtracting a smaller theoretical circle. |
| 534 | +<strong style="margin:12px;">Derived from the area by subtracting a smaller theoretical circle. |
523 | 535 | <br> |
524 | 536 | <br> |
525 | 537 | Formula: C = 6.4 × radius |
526 | | -</p> |
| 538 | +</strong> |
| 539 | +<br> |
527 | 540 | <br> |
528 | 541 | <a style="margin:7px;" href="#sphere">Volume of a Sphere</a> |
529 | 542 | <br> |
530 | | -<p style="margin:12px;">Compared to a cube, using the area of the sphere's cross-section. |
| 543 | +<strong style="margin:12px;">Compared to a cube, using the area of the sphere's cross-section. |
531 | 544 | <br> |
532 | 545 | <br> |
533 | 546 | Formula: V = cubic value of ( square root ( 3.2 ) × radius ) |
534 | | -</p> |
| 547 | +</strong> |
| 548 | +<br> |
535 | 549 | <br> |
536 | 550 | <a style="margin:7px;" href="#cone">Volume of a Cone</a> |
537 | 551 | <br> |
538 | | -<p style="margin:12px;">Compared to an octant sphere and a quarter cylinder. |
| 552 | +<strong style="margin:12px;">Compared to an octant sphere and a quarter cylinder. |
539 | 553 | <br> |
540 | 554 | <br> |
541 | 555 | Formula: V = 3.2 × ( square value of the radius ) × height, divided by square root ( 8 ) |
542 | | -</p> |
| 556 | +</strong> |
| 557 | +<br> |
543 | 558 | <br> |
544 | 559 | <br> |
545 | 560 | <h4 style="margin:7px;">Comparative Geometry</h4> |
546 | | -<p style="margin:12px;">Using geometric relationships to derive areas and volumes. |
547 | | -</p> |
| 561 | +<strong style="margin:12px;">Using geometric relationships to derive areas and volumes. |
| 562 | +</strong> |
| 563 | +<br> |
548 | 564 | <br> |
549 | 565 | <h4 style="margin:7px;">Scaling and Proportions</h4> |
550 | | -<p style="margin:12px;">Applying proportional relationships for accurate calculations. |
551 | | -</p> |
| 566 | +<strong style="margin:12px;">Applying proportional relationships for accurate calculations. |
| 567 | +</strong> |
| 568 | +<br> |
552 | 569 | <br> |
553 | 570 | <h4 style="margin:7px;">Algebraic Manipulation</h4> |
554 | | -<p style="margin:12px;">Simplifying equations to ensure consistency and precision. |
555 | | -</p> |
| 571 | +<strong style="margin:12px;">Simplifying equations to ensure consistency and precision. |
| 572 | +</strong> |
556 | 573 | </section> |
557 | 574 | <br> |
558 | 575 | <br> |
@@ -3165,7 +3182,7 @@ <h4 style="margin:12px;">Archimedes and the Polygonal Trap</h4> |
3165 | 3182 | 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. |
3166 | 3183 | <br> |
3167 | 3184 | <br> |
3168 | | -<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. |
| 3185 | +<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> |
3169 | 3186 | </p> |
3170 | 3187 | </section> |
3171 | 3188 | <br> |
@@ -3296,10 +3313,11 @@ <h4 style="margin:12px;">A Rational Alternative: 3.2</h4> |
3296 | 3313 | 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. |
3297 | 3314 | <br> |
3298 | 3315 | <br> |
3299 | | -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. |
| 3316 | +<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. |
3300 | 3317 | <br> |
3301 | 3318 | <br> |
3302 | 3319 | 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. |
| 3320 | +</strong> |
3303 | 3321 | <br> |
3304 | 3322 | <br> |
3305 | 3323 | These are two aspects of that. |
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