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@@ -365,7 +365,7 @@ <h1 style="font-size:160%;margin:7px;">How Accurate Are The Conventional Geometr
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The symbol π was introduced because the true ratio—approximately 3.14159…—is an infinite fraction. Since we can’t write all its digits, we needed a symbol. But this symbol has taken on a life of its own.
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Technically, the circumference is a perimeter. So the ratio ( P / d ) ( perimeter over diameter ) became π/δ in Greek. With ( d = 1 ), we get ( π / 1 = π ). But this is not necessarily the ratio itself—it’s the notation of that ratio. That distinction matters. There was a ratio between circumference and diameter long before the Greeks studied it. We must not let their symbolic shortcut overwrite a more fundamental geometric truth.
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Technically, the circumference is a perimeter. So the ratio ( P / d ) ( perimeter over diameter ) became π / δ in Greek. With ( d = 1 ), we get ( π / 1 = π ). But this is not necessarily the ratio itself—it’s the notation of that ratio. That distinction matters. There was a ratio between circumference and diameter long before the Greeks studied it. We must not let their symbolic shortcut overwrite a more fundamental geometric truth.
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It was not until the 18th century that the symbol π, popularized by the mathematicians of the time, gained widespread acceptance.
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But this is not a magical formula—it’s a symbolic summary of prior assumptions. Each notation should correspond to a real, logical property of the circle. Yet upon inspection, inconsistencies emerge. The formula doesn’t derive the circumference from first principles; it assumes it.
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Calculus can be a useful mathematical tool, but it calling it exact is a bold statement.
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Calculus can be a useful mathematical tool, but calling it exact is a bold statement.
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It can be exact with exact limits and basic operations, but if those are given then they can be calculated directly without calculus.
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<pstyle="margin:12px;"><b>φ The golden ratio:</b>
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<pstyle="margin:12px;"><b>φ The Golden Ratio:</b>
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Some relate the numeric value of 3.14… to the so-called “golden ratio” of ( √5 + 1 ) / 2.
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<b>A Rational Alternative: 3.2</b>
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Historical records suggest that a legislative process took place in 1897, Indiana, USA, known as House Bill 246, or Indiana Pi Act, aiming to replace the numeric value 3.14 by 3.2.
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Historical records suggest that a legislative process took place in 1897, Indiana, USA, known as House Bill 246 ( sometimes listed as 264 ), or Indiana Pi Act, aiming to replace the numeric value 3.14 by 3.2.
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Unfortunately, the exact details of the proposed method in the Indiana Pi Bill are somewhat obscure and have been interpreted differently by various accounts.
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