Update index.html

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Author: Gmac4247

index.html

@@ -2599,17 +2599,11 @@ <h4>Archimedes and the Illusion of Limits</h4>
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 is not a deep theorem — it is simply a geometric tautology arising from symmetry.
 <br><br>
-But Euclid stops there.</p>
-<br>
-<p><strong>Euclid gives exact angle bisection as a geometric construction, but he provides no computational framework for evaluating the sine of the bisected angles.</strong> 
+The angles 22.5°, 15° and 7.5° can be constructed by subtracting a triangle from a known triangle, but Euclid stops there.
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-The angles 22.5°, 7.5°, and 3.75° can all be constructed with compass and straightedge, yet the numerical values of</p>
-<ul style="margin:6px">
-	<li>sin(22.5°)</li>
-      <li>sin(7.5°)</li>
-      <li>sin(3.75°)</li>
-</ul>
-<p>cannot be derived from Euclid’s axioms or propositions.
+Euclid gives exact angle bisection as a geometric construction, but he provides no computational framework for evaluating the sine of the bisected angles.
+<br>
+Any angle can be bisected with compass and straightedge, yet — with a few exceptions — their numerical values cannot be derived from Euclid’s axioms or propositions.
 <br>
 Any method for computing these values requires additional, non‑Euclidean assumptions, that were added centuries later:</p>
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