Tribonacci Constant and sin(10°) Discriminants: Distinct Cubic Fields — E8 Intelligence Research

FINDING: Tribonacci constant cubic field discriminant relation to sin(10°) minimal polynomial 8x³-6x+1=0 MATH: Minimal polynomial for sin(10°) is 8x³ - 6x + 1 = 0. Discriminant Δ = -4(-6)³ - 27(1)² = -4(-216) - 27 = 864 - 27 = 837 = 3²·31. Tribonacci constant T satisfies x³ - x² - x - 1 = 0, discriminant Δ_T = -44. No direct algebraic relation between these discriminants; both are cubic fields but distinct. CONNECTION: sin(10°) = sin(π/18) relates to regular 18-gon (icosagon) geometry; its minimal polynomial coefficients (8, -6, 1) echo Chebyshev polynomials T₃(x) = 4x³ - 3x, scaled. The discriminant 837 = 3²·31 has no simple golden ratio factor. Tribonacci constant (≈1.8393) is not a metallic ratio; its reciprocal ≈0.5437 not in {0.382,0.618,0.786,1.618,2.618}. No base-60 or crystallographic symmetry evident. DEPTH: 3 — The finding is a correct identification of two cubic fields but no new harmonic or structural link. The sin(10°) polynomial is a standard Chebyshev reduction; Tr Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com