Mathematical framework links harmonic ratios to natural structures, suggesting universal patterns in geometry.
This paper develops a unified mathematical explanation for the dominance of the harmonic ratios √2, √3, and φ across natural structures — from planetary orbits to biological growth patterns. Using the Qindra Core advanced resonance model, it demonstrates that these ratios arise from stable geometric energy minima, nonlinear vibrational alignment, and universal harmonic boundary conditions. The results provide a physics-consistent framework that connects natural geometry with planetary resonance mechanics.
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Radhakrishnan Jayaraman (2025) studied this question.
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