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Home » "Sliding Glass Dance? Install This Cat Door and Watch Them Roam Freely! - High Altitude Science

"Sliding Glass Dance? Install This Cat Door and Watch Them Roam Freely! - High Altitude Science

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 \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}.

📌 But we need a closed-form expression in terms of \( z \) and \( c \). However, consider a known result:

📌 In a right triangle, \( r = \frac{a + b - c}{2} \), and \( c = \text{hypotenuse} \). But there's a known ratio:

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