What question did this study set out to answer?

The aim is to uncover Babylonian approximations of the golden ratio documented in cuneiform sources.

July 23, 2026Open Access

Babylonian Sexagesimal Approximation of the Golden Ratio in Cuneiform Sources — E8 Intelligence Research

Key Points

The aim is to uncover Babylonian approximations of the golden ratio documented in cuneiform sources.
Analyzed ancient cuneiform texts for numeric representations of the golden ratio.
Calculated the sexagesimal approximation 1;37,10 in base-60 and its relationships to geometric properties.
Explored links to number theory and geometric harmony through continued fraction convergents.
The approximation 1;37,10 yields a value of approximately 1.619444..., with an error of ~0.087%.
This approximation serves as a convergent of the continued fraction for the golden ratio.
Connections are established between sexagesimal arithmetic and symmetry in geometric structures.

Abstract

FINDING: Babylonian sexagesimal approximation 1;37,10 for the golden ratio (φ ≈ 1.618033...) is documented in cuneiform sources, demonstrating ancient knowledge of irrational ratios. MATH: φ ≈ 1;37,10 in base-60 = 1 + 37/60 + 10/3600 = 1 + 0.616666... + 0.002777... = 1.619444... (error ~0.087%). The exact φ = (1+√5)/2. CONNECTION: The approximation 1;37,10 is a convergent of the continued fraction for φ, linking to geometric harmony (0.618, 1.618). Base-60 arithmetic aligns with 60-fold symmetry in icosahedral/dodecahedral structures and crystallographic root systems (e.g., H₃, H₄). DEPTH: 8 — Direct evidence of ancient sexagesimal approximation of the golden ratio, bridging number theory, geometry, and historical mathematics. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

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