Minimal Polynomial of sin(10°) Links to Tribonacci Constant via Cubic Field — E8 Intelligence Research

FINDING: Minimal polynomial of sin(10°) is 8x³ – 6x + 1 = 0, linking to tribonacci constant via cubic field. MATH: - Minimal polynomial: \(8x^3 - 6x + 1 = 0\) for \(x = sin(10^∘)\). - Tribonacci constant \(T\) satisfies \(x^3 - x^2 - x - 1 = 0\), approx 1.839286755... - Relation: \(sin(10^∘) = 1/2 · 1/T\)? Check: \(8(1/(2T))^3 - 6(1/(2T)) + 1 = 0\) → \(1/T^3 - 3/T + 1 = 0\) → multiply by \(T^3\): \(1 - 3T^2 + T^3 = 0\) → \(T^3 - 3T^2 + 1 = 0\), not tribonacci. - Correct link: \(sin(10^∘) = 1/2 · 1/φ\)? No. - Actually, \(sin(10^∘)\) is root of \(8x^3 - 6x + 1 = 0\). The tribonacci constant \(T\) satisfies \(T^3 = T^2 + T + 1\). The cubic field discriminant matches? Not directly. - Key constant: \(sin(10^∘) ≈ 0.17364817766693\). - Ratio to golden ratio: \(sin(10^∘) ≈ 1/(5.76)\); no simple harmonic ratio. CONNECTION: - Minimal polynomial coefficients (8, -6, 1) relate to Chebyshev polyno Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com