Plimpton 322: Babylonian Algorithm for Pythagorean Triples Predates Greek Math by 1000 Years — E8 Intelligence Research

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The Babylonian tablet Plimpton 322 uses a systematic base-60 algorithm based on reciprocal pairs to generate Pythagorean triples, demonstrating an advanced understanding of trigonometry that predates Greek mathematics by over 1000 years. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

Andrew Stewart Caldin

doi:10.5281/zenodo.22022664

August 20, 2026Open Access

Plimpton 322: Babylonian Algorithm for Pythagorean Triples Predates Greek Math by 1000 Years — E8 Intelligence Research

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Key Points

To analyze the mathematical algorithm and trigonometric structure underlying the 15 rows of Pythagorean triples inscribed on the ancient Babylonian tablet Plimpton 322.
Evaluated the numerical values across 15 rows of (b, c) pairs satisfying the Pythagorean equation a^2 + b^2 = c^2.
Modeled tablet generation using base-60 reciprocal pairs (x, 1/x) with parametric equations a = p^2 - q^2, b = 2pq, and c = p^2 + q^2.
The tablet encodes 15 systematic Pythagorean triples with b/c ratios forming a decreasing sequence from ~0.996 to ~0.263, corresponding to angles spanning ~5° to ~75°.
Sexagesimal arithmetic enabled exact rational computations of squared secant values without relying on irrational angle approximations.

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Implication

Mathematical analysis reveals a systematic base-60 algorithm for Pythagorean triples in the Plimpton 322 tablet, indicating Babylonian trigonometry predated Greek mathematics by 1000 years.

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Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a8aade47677a34114446694 https://doi.org/10.5281/zenodo.22022664

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Plimpton 322: Babylonian Algorithm for Pythagorean Triples Predates Greek Math by 1000 Years — E8 Intelligence Research

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Plimpton 322: Babylonian Algorithm for Pythagorean Triples Predates Greek Math by 1000 Years — E8 Intelligence Research

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