Antikythera Mechanism's Gear Ratios Decode Lunar-Solar Cycles via Continued Fractions — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: The Antikythera Mechanism encodes lunar-solar cycles via a 223-month Saros dial, 19-year Metonic cycle, and 76-year Callippic cycle, with gear ratios derived from continued fractions of astronomical periods. | MATH: Saros = 223 synodic months ≈ 242 draconic months ≈ 239 anomalistic months; Metonic = 235 synodic months = 19 tropical years; Callippic = 4×Metonic = 76 years; gear ratio for lunar phase: 64:38 (or 32:19) approximates 2.085 (actual synodic/anomalistic ratio ≈ 2.085); the 53-tooth gear (fragment C) yields 53/19 ≈ 2.789, linked to the Metonic cycle's 235/19 = 12.368 lunations/year. | CONNECTION: The 235:19 ratio is a convergent of the continued fraction for the lunar month/year ratio (12.368266...), whose convergents include 12, 12⅓, 12⅜, 12⁴⁄₁₁ — the mechanism uses 235/19 (error ~0.0003 days/year). The 223-month Saros is 18 years + 11⅓ days, aligning with the 0.618 golden-ratio-adjacent 11.3-day shift (not exact, but the 3:2 ratio of Saros to Metonic (223/235 ≈ 0.949 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204268363
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