Golden Ratio Map's Linear Convergence Rate Tied to Coxeter Dihedral Symmetry — E8 Intelligence Research

August 9, 2026Open Access

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Key Points

This research examines the linear convergence rate of the golden ratio map and its relation to Coxeter group symmetry.
Investigated fixed-point iteration using the function g(x) = 1 + 1/x.
Analyzed convergence rate and asymptotic error constant at the golden ratio fixed point.
Explored the relationship with the H₂ Coxeter group's dihedral symmetry.
Identified the linear convergence rate as governed by the asymptotic constant 1/φ² ≈ 0.382.
Established a direct link between the golden ratio and the H₂ Coxeter group's dihedral symmetry.
Highlighted the role of this constant in fixed-point iteration and its reflection in pentagonal tilings.

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Finding reveals the linear convergence of the golden ratio map linked to Coxeter dihedral symmetry, suggesting deeper mathematical connections.

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Andrew Stewart Caldin (2026) studied this question.

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