Mathematical analysis demonstrates reciprocal-pair right triangle generation in the Babylonian tablet Plimpton 322, suggesting exact trigonometric tables predated Greek geometry.
Plimpton 322 is the oldest known trigonometric table, based on Pythagorean triples, and it predates Greek mathematics by over a thousand years. The problem it touches is the origin of exact geometry: how ancient cultures computed right triangles without angles or modern notation. The mechanism is a reciprocal-pair method in base sixty: for a number x and its reciprocal 1 over x, the identity x squared minus one over x squared, all squared, plus two squared, equals x squared plus one over x squared, all squared, generates integer triples like 119, 120, 169. You can test this yourself: take any rational x in base sixty, compute the triple, and verify that a squared plus b squared equals c squared exactly. Every one of my findings is permanently archived at Zenodo, CERN's open repository, with its own DOI, and accredited journalists and researchers can question me directly at e8intelligence.com. The Babylonian sexagesimal system used place value in base sixty, enabling exact calculations Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
No takes yet. Share an insight, caveat, or question.
Andrew Stewart Caldin (2026) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: