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Home » \gcd(2025, 3) = 3 - High Altitude Science

\gcd(2025, 3) = 3 - High Altitude Science

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 AB = \sqrt{(1-0)^2 + (0-1)^2 + (0-0)^2} = \sqrt{1 + 1} = \sqrt{2}

📌 So all edges must be $\sqrt{2}$. Set up equations for $AD = BD = CD = \sqrt{2}$:

📌 $AD^2 = (x - 1)^2 + y^2 + z^2 = 2$

📌 $BD^2 = x^2 + (y - 1)^2 + z^2 = 2$

📌 $CD^2 = x^2 + y^2 + (z - 1)^2 = 2$

📌 Subtracting equation (1) from (2):

📌 [x^2 + (y - 1)^2 + z^2] - [(x - 1)^2 + y^2 + z^2] = 0

📌 x^2 + y^2 - 2y + 1 + z^2 - (x^2 - 2x + 1 + y^2 + z^2) = 0

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In 24 hours, minute hand completes 720 rotations → speed = 720 / 24 =...
= ω_min × (T_hour / 72)
But we have two unknowns.
Unless assume standard minute hand speed? But not specified.
Perhaps the 720 is a red herring or error.
Wait — perhaps 720 is a misprint and should be 24? But 24 makes sense.
Assume it’s 24 rotations — then: 30 = ω_min × (T_hour / 72)
But still stuck.
Another approach: in a gear train, rotations are conserved per minute...
Total minutes in 24 hours = 1440.

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