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Home » From Fractions to Decimals: The Surprising Value of 5/6 Revealed! - American Beagle Club

From Fractions to Decimals: The Surprising Value of 5/6 Revealed! - American Beagle Club

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 However, there is a known simplification:

📌 Using \( A = c \cdot s \), and \( s = \frac{a + b + z}{2} \), but for a right triangle, it can be shown that:

📌 \frac{\text{Area of circle}}{\text{Area of triangle}} = \frac{\pi c^2}{c \cdot s} = \frac{\pi c}{s}.

📌 But we aim to express in terms of \( z \) and \( c \) only. However, without loss of generality, use a standard identity:

📌 For a right triangle,

📌 c = \frac{a + b - z}{2}, \quad A = \frac{1}{2}ab = \frac{(a + b)^2 - z^2}{4} \cdot \text{wait — better: }

📌 Alternatively, recall that \( A = r s = c s \), so:

📌 \frac{\pi c^2}{A} = \frac{\pi c^2}{c s} = \frac{\pi c}{s}.

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