Saros Cycle: Near-Exact Lunar Resonance, No Golden Ratio Connection — E8 Intelligence Research

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The Saros cycle is based on a near-exact rational integer resonance of lunar periods (223 synodic, 242 draconic, and 239 anomalistic months) and possesses no mathematical connection to the golden ratio or irrational harmonics. Novelty: ClaimNovelty.CONFIRMATORY. Consensus alignment: ConsensusAlignment.NEUTRAL.

Andrew Stewart Caldin

doi:10.5281/zenodo.22732511

September 13, 2026Open Access

Saros Cycle: Near-Exact Lunar Resonance, No Golden Ratio Connection — E8 Intelligence Research

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Key Points

To determine whether the astronomical Saros cycle incorporates the golden ratio, crystallographic symmetry, or unique sexagesimal patterns within its orbital alignments.
Evaluated the period lengths of 223 synodic months (6585.3211 days), 242 draconic months (6585.3575 days), and 239 anomalistic months (6585.5376 days).
Calculated pairwise integer ratios and base-60 decompositions to test for geometric proportions or irrational constants.
Direct ratio calculations yielded 223/242 = 0.9215, 242/223 = 1.0852, and 239/223 = 1.0717, showing zero appearance of the golden ratio (1.618) or its derivatives (0.382, 0.786).
Decomposition into base-60 components (223 = 3×60 + 43; 242 = 4×60 + 2; 239 = 3×60 + 59) revealed standard integer remainders with no structural sexagesimal elegance.
Characterized the Saros cycle strictly as a rational integer resonance (223:242:239) rather than an irrational or crystallographic harmonic.

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Implication

Mathematical analysis reveals rational integer resonance in lunar eclipse periods, demonstrating an absence of golden ratio harmonics or structural base-60 elegance.

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Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6aa7dfc60926e14a848b3dba https://doi.org/10.5281/zenodo.22732511

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Saros Cycle: Near-Exact Lunar Resonance, No Golden Ratio Connection — E8 Intelligence Research

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Saros Cycle: Near-Exact Lunar Resonance, No Golden Ratio Connection — E8 Intelligence Research

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