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To derive the fine structure constant from golden ratio geometry and explore its significance.

March 8, 2026Open Access

The Fine Structure Constant and the Golden Angle: α ≈ φ²/360 as a Geometric Identity

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To derive the fine structure constant from golden ratio geometry and explore its significance.
Derivation of the fine structure constant from geometric principles related to the golden ratio.
Calculation of α⁻¹ based on φ²/360.
Evaluation of residual errors and their connection to quantum electrodynamics (QED).
Derived fine structure constant α⁻¹ is approximately 137.51.
Calculated using the relationship α⁻¹ ≈ φ²/360.
Observed 0.34% residual, indicating small potential for QED corrections.

Abstract

We derive the fine structure constant α from golden ratio geometry, obtaining α⁻¹ ≈ φ²/360 = 137.51 as the zeroth-order result with a 0.34% residual amenable to QED correction.

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Pei-Yuan Ju (Sat,) studied this question.

www.synapsesocial.com/papers/69ada892bc08abd80d5bbb30 — DOI: https://doi.org/10.5281/zenodo.18899269

The Fine Structure Constant and the Golden Angle: α ≈ φ²/360 as a Geometric Identity

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