tetrahedralAngleDegrees
plain-language theorem explainer
The declaration supplies the tetrahedral bond angle in degrees by scaling arccos(-1/3) by the factor 180/π. Chemists working with Recognition Science molecular geometries cite it when predicting structures for methane, ammonia, and water. The definition is a direct unit-conversion wrapper from the radian precursor.
Claim. The tetrahedral bond angle in degrees equals $arccos(-1/3) · (180/π)$.
background
The module derives bond angles from the φ-lattice by minimizing J-cost for n equivalent bonds around a central atom, giving the rule cos(θ) = -1/(n-1). For tetrahedral geometry (n=4) this produces cos(θ) = -1/3, hence θ = arccos(-1/3) in radians. The upstream definition tetrahedralAngleRadians supplies exactly this radian value as Real.arccos(-1/3). The module document notes the φ-connection via the dodecahedron and the bias proxy 1 - 1/φ.
proof idea
One-line wrapper that multiplies the radian tetrahedral angle by the conversion constant 180/π.
why it matters
This definition is used directly by the methane, water, and ammonia angle predictions in the same module. It populates the geometry table (linear 180°, trigonal 120°, tetrahedral 109.47°, octahedral 90°) that follows from the RS mechanism of minimizing repulsion while preserving bond strength. The result sits inside the D=3 spatial setting and the eight-tick octave of the forcing chain.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.