methaneAngle
plain-language theorem explainer
Methane bond angle is defined as the tetrahedral angle of arccos(-1/3) converted to degrees. Molecular chemists comparing RS lattice predictions to CH4 geometry would cite this alias. The definition is a direct one-line reference to the precomputed tetrahedral value.
Claim. The bond angle in methane (CH₄) equals the tetrahedral angle θ where cos(θ) = -1/3, or θ ≈ 109.47°.
background
The module derives bond angles from the φ-lattice by minimizing J-cost for n equivalent bonds around a central atom. For tetrahedral geometry with n=4 the cosine formula yields cos(θ) = -1/(n-1) = -1/3, giving θ = arccos(-1/3) ≈ 109.47°. The φ-connection enters via the dodecahedron and the bias proxy 1 - 1/φ that measures deviation from linearity. Upstream, tetrahedralAngleDegrees converts the radian form (itself based on the -1/3 cosine) to degrees via multiplication by 180/π.
proof idea
One-line wrapper that applies tetrahedralAngleDegrees.
why it matters
This definition slots methane into the RS bond-angle table for n=4 geometry inside the φ-lattice framework. It supports the module's predictions for linear, trigonal, tetrahedral and octahedral cases that arise from the same J-cost minimization. The placement ties directly to the tetrahedral cosine result and the overall φ-ladder structure for molecular geometries.
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