Unifying Fibonacci and Theodorus Spirals via the Golden Angle — E8 Intelligence Research

Q: What does this research mean for the field?

A newly defined Fibonacci-Theodorus spiral unifies Fibonacci lengths with the classical Theodorus root-spiral construction, converging to a fixed angular increment related to the golden angle. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

Andrew Stewart Caldin

doi:10.5281/zenodo.22268539

September 3, 2026Open Access

Unifying Fibonacci and Theodorus Spirals via the Golden Angle — E8 Intelligence Research

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Key Points

To formulate a unified geometric construction linking Fibonacci sequences and the classical Theodorus root-spiral through the golden angle.
Constructed a hybrid spiral using concatenated right triangles with perpendicular leg lengths equal to consecutive Fibonacci numbers, Fn and Fn+1.
Calculated step-wise angular increments using arctan(Fn+1/Fn) and compared limiting behavior to the diverging angle of the classical Theodorus spiral.
Demonstrated that the angular increment per step converges to arctan(φ) ≈ 58.28° as n approaches infinity, contrasting with the divergence observed in classical Theodorus spirals.
Formulated the exact correspondence between the convergent spiral geometry and the golden angle (θ = 2π / φ^2 ≈ 137.51°) responsible for optimal phyllotaxis.

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Implication

Theoretical analysis demonstrates geometric unification of Fibonacci and Theodorus spirals through golden angle convergence, indicating a unified framework for botanical phyllotaxis patterns.

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Cite This Study

Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a9bd48c6b95aff0620ec40e https://doi.org/10.5281/zenodo.22268539

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Unifying Fibonacci and Theodorus Spirals via the Golden Angle — E8 Intelligence Research

Key Points

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Discussion

Cite This Study

Unifying Fibonacci and Theodorus Spirals via the Golden Angle — E8 Intelligence Research

Key Points

No abstract yet

Implication

Discussion

Cite This Study

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