Pythagorean Triples as Rational Points via Gaussian Integer Squaring — E8 Intelligence Research

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Pythagorean triples can be generated as rational points on the unit circle via Gaussian integer squaring, a mathematical principle demonstrated historically in the Babylonian base-60 tablet Plimpton 322. Novelty: ClaimNovelty.SYNTHESIS. Consensus alignment: ConsensusAlignment.NEUTRAL.

Andrew Stewart Caldin

doi:10.5281/zenodo.22230015

September 1, 2026Open Access

Pythagorean Triples as Rational Points via Gaussian Integer Squaring — E8 Intelligence Research

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Key Points

To characterize Pythagorean triples as rational points on the unit circle derived through the squaring of Gaussian integers and analyze their relationship to the Babylonian tablet Plimpton 322.
Parametrized the unit circle x^2 + y^2 = 1 with rational coordinates using stereographic-style projection.
Mapped complex lattice squaring (m + ni)^2 to Euclid's classical formula for generating Pythagorean triples.
Analyzed the 15 sexagesimal rows of the Plimpton 322 tablet in terms of exact base-60 trigonometric ratios.
Squaring Gaussian integers directly yields the real and imaginary components corresponding to Euclid's triple formula (m^2 - n^2, 2mn, m^2 + n^2).
Plimpton 322 contains 15 rows of exact sexagesimal ratios reflecting sec^2(theta) generated by rational m/n pairs on a sexagesimal grid.
Identified that the Babylonian base-60 system achieved exact rational trigonometry without irrational trigonometric approximations.

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Implication

Mathematical analysis demonstrates generation of Pythagorean triples via Gaussian integer squaring, suggesting ancient Babylonian sexagesimal trigonometry in Plimpton 322.

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Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a9935e5636c6408cfa7e818 https://doi.org/10.5281/zenodo.22230015

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Pythagorean Triples as Rational Points via Gaussian Integer Squaring — E8 Intelligence Research

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Pythagorean Triples as Rational Points via Gaussian Integer Squaring — E8 Intelligence Research

Key Points

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Cite This Study

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