Babylonian Base-60 Math: Exact Fractions, Reciprocal Pairs, and Plimpton 322's Golden Ratio Link — E8 Intelligence Research

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Babylonian base-60 positional notation encodes exact fractions and yields a direct mathematical link to the golden ratio (1/φ) via a repeating sexagesimal pattern, while naturally encoding hexagonal and trigonal symmetry. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

Andrew Stewart Caldin

doi:10.5281/zenodo.22075775

August 24, 2026Open Access

Babylonian Base-60 Math: Exact Fractions, Reciprocal Pairs, and Plimpton 322's Golden Ratio Link — E8 Intelligence Research

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Key Points

Investigate the mathematical structure of the ancient Babylonian base-60 sexagesimal system, including reciprocal pairs, Plimpton 322 Pythagorean triples, and connections to the golden ratio.
Analyzed base-60 positional notation place values, exact fractions, and reciprocal pairs.
Evaluated 15 rows of integer Pythagorean triples and tangent ratio approximations from the Plimpton 322 tablet.
Calculated the base-60 fractional expansion of the inverse golden ratio (1/φ) and correlated it with triangular and circular geometric symmetries.
Demonstrated that the reciprocal golden ratio 1/φ (≈ 0.6180339) yields the repeating sexagesimal expansion 0;36,36,36... in base-60.
Identified that Plimpton 322 contains 15 rows of integer Pythagorean triples with ratios approximating tangents for angles from ~45° to ~30°.
Showed that base-60 positional notation intrinsically mirrors hexagonal and trigonal symmetries derived from 60° equilateral triangles and 360° circles.

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Mathematical analysis demonstrates sexagesimal representations of reciprocal pairs, Pythagorean triples, and the golden ratio, highlighting structural geometric symmetries in ancient Babylonian...

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Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a8e9bae451774b83f3b4861 https://doi.org/10.5281/zenodo.22075775

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Babylonian Base-60 Math: Exact Fractions, Reciprocal Pairs, and Plimpton 322's Golden Ratio Link — E8 Intelligence Research

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Babylonian Base-60 Math: Exact Fractions, Reciprocal Pairs, and Plimpton 322's Golden Ratio Link — E8 Intelligence Research

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