Update index.html

disambiguatingDescription

Author: Gmac4247

index.html

@@ -2588,10 +2588,11 @@ <h4>Archimedes and the Illusion of Limits</h4>
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 <p>The Greek Archimedes’ method for estimating the pi is often celebrated as a foundational triumph of geometric reasoning.</p>
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 <summary itemprop="disambiguatingDescription">The pi is actually an approximation derived from limits. But that method itself introduced compounding errors.</summary>
-<p>Archimedes approximated the circumference using inscribed and circumscribed polygons. He began with a circle bounded by an inscribed and a circumscribed hexagon — not the absolute minimum of 3 or 4 sides — likely because the hexagon is closer to the circle while still being easily calculable. By bisecting the angles (splitting them in half), he turned the hexagons into a 12-gons, then 24-gons, all the way to 96-sided shapes. This allowed him to calculate the perimeter of these shapes using only straight lines and Pythagoras' theorem. 
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+<p>Archimedes approximated the circumference using inscribed and circumscribed polygons. He began with a circle bounded by an inscribed and a circumscribed hexagon — not the absolute minimum of 3 or 4 sides — likely because the hexagon is closer to the circle while still being easily calculable. By bisecting the angles (splitting them in half), he turned the hexagons into a 12-gons, then 24-gons, all the way to 96-sided shapes. This allowed him to calculate the perimeter of these shapes in terms of the diameter using only straight lines and Pythagoras' theorem. 
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 Observing how the difference between the two polygonal perimeters — one inside the circle, one outside — became smaller, Archimedes likely believed that as the number of sides increased, the difference between the perimeters of the inscribed and circumscribed polygons would converge toward zero, approaching the circumference of the circle.