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The Lobachevsky parallelism function at distance ln φ equals arctan(2). Proved via double angle formula and verified via arccos form. Both give 1/√5. Branch-safe. No dependencies.
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Title CCFU Proof 13 — Parallelism Identity Π(ln φ) = arctan(2)
The Lobachevsky parallelism function at distance ln φ equals arctan(2). Proved via double angle formula and verified via arccos form. Both give 1/√5. Branch-safe. No dependencies.
Work type Research papers, Thesis, Lecture notes
Tags golden ratio, proof, lobachevsky, mathematics, ccfu, parallelism, arctan, hyperbolic geometry
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Identifier 2605165676497
Entry date May 16, 2026, 6:41 PM UTC
License All rights reserved
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