Golden Angle Governs Phyllotaxis via Continued-Fraction Packing Efficiency — E8 Intelligence Research

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Phyllotaxis is governed by the golden angle, which maximizes seed packing efficiency through continued-fraction convergence. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

Andrew Stewart Caldin

doi:10.5281/zenodo.22122211

August 27, 2026Open Access

Golden Angle Governs Phyllotaxis via Continued-Fraction Packing Efficiency — E8 Intelligence Research

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Key Points

Determine how the golden angle and continued-fraction convergence govern botanical phyllotaxis and maximize packing efficiency.
Calculated geometric divergence parameters using the golden angle (θ ≈ 137.507764° or 2π/φ² radians) derived from the golden ratio (φ ≈ 1.6180339887).
Evaluated the continued-fraction expansion of the inverse golden ratio (φ⁻¹ = [0;1,1,1,...]) and its successive Fibonacci convergents (Fn+1/Fn).
Demonstrated that the golden angle divergence of approximately 137.507764° provides the mathematical optimum for rotational packing efficiency.
Identified that the convergence of consecutive Fibonacci number ratios toward φ minimizes radial alignment gaps, maximizing space utilization.

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Implication

Theoretical analysis reveals optimal seed packing in botanical phyllotaxis, indicating that the golden angle maximizes density via continued fractions.

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Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a92996e8e5d7d1fc0c1157a https://doi.org/10.5281/zenodo.22122211

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Golden Angle Governs Phyllotaxis via Continued-Fraction Packing Efficiency — E8 Intelligence Research

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Golden Angle Governs Phyllotaxis via Continued-Fraction Packing Efficiency — E8 Intelligence Research

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