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Spin-down probability = 1 - 0.75 = <<1-0.75=0.25>>0.25 - go-checkin.com

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 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:

📌 Actually, a cleaner approach:

📌 Let the triangle have legs \( a, b \), hypotenuse \( z \). Then:

📌 A = \frac{ab}{2}, \quad s = \frac{a + b + z}{2}, \quad r = \frac{a +

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Recall the relationships between spherical and Cartesian coordinates:
x =
ho \sin\phi \cos heta, \quad y =
ho \sin\phi \sin heta, \quad z =
ho \cos\phi
Substitute \(
ho = c \sin(\phi)\) into the expressions:
x = c \sin(\phi) \cdot \sin(\phi) \cos heta = c \sin^2(\phi) \cos heta
y = c \sin^2(\phi) \sin heta
z = c \sin(\phi) \cos(\phi)

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