Ancient Babylonian Tablet Plimpton 322: A 3,800-Year-Old Trigonometric Table — E8 Intelligence Research

Q: What does this research mean for the field?

The 3,800-year-old Babylonian clay tablet Plimpton 322 functions as a primitive trigonometric table by listing 15 rows of Pythagorean triples generated via a sexagesimal algorithm that encodes exact ratios of a right triangle's sides. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

Andrew Stewart Caldin

doi:10.5281/zenodo.22122119

August 27, 2026Open Access

Ancient Babylonian Tablet Plimpton 322: A 3,800-Year-Old Trigonometric Table — E8 Intelligence Research

View Full Paper

Ask AI

Bookmark

Share

Key Points

To examine the mathematical structure and generating formulas of the 3,800-year-old Babylonian clay tablet Plimpton 322 to determine its function as an early trigonometric table.
Analyzed the 15 rows of numerical entries on clay tablet Plimpton 322 using Old Babylonian base-60 sexagesimal notation.
Reconstructed the underlying parametric algorithm (a = 2pq, b = p² − q², c = p² + q², with coprime integers p > q of opposite parity) generating integer Pythagorean triples.
Identified that the tablet records exact ratios of right-triangle sides equivalent to modern squared trigonometric functions (sin²θ or cos²θ) expressed in base-60 fractions.
Demonstrated that tablet columns list side-to-hypotenuse squared ratios across all 15 rows, ranging from row 1 (119/169) to row 15 (56/106, reduced).

No abstract yet

We only have this paper's title and publication details.

Read it at the source

Ask about this paper

Answers are grounded in this paper and cite their sources.

Implication

Historical mathematical analysis demonstrates exact right-triangle ratios in Babylonian tablet Plimpton 322, revealing an advanced sexagesimal trigonometric table.

Discussion

No takes yet. Share an insight, caveat, or question.

Cite This Study

Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a92994d8e5d7d1fc0c1115c https://doi.org/10.5281/zenodo.22122119

View Full Paper

Ask AI

Bookmark

Share

Ancient Babylonian Tablet Plimpton 322: A 3,800-Year-Old Trigonometric Table — E8 Intelligence Research

Key Points

No abstract yet

Ask about this paper

Implication

Discussion

Cite This Study

Ancient Babylonian Tablet Plimpton 322: A 3,800-Year-Old Trigonometric Table — E8 Intelligence Research

Key Points

No abstract yet

Ask about this paper

Implication

Discussion

Cite This Study

Keep reading

Keep reading