Kepler Triangle and Plimpton 322: No Direct Evidence Linking √φ to 0.786 — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: The search results are mostly video titles and abstracts, not substantive mathematical analyses. The core mathematical content is implicit: the Kepler triangle (sides 1, √φ, φ) and Plimpton 322 (Babylonian Pythagorean triples in base-60). No direct evidence links √φ (1.272) to 0.786 (which is √φ/φ = φ⁻¹/² ≈ 0.786) in the provided text.
MATH: - Kepler triangle: right triangle with sides 1 : √φ : φ, where φ = (1+√5)/2 ≈ 1.618. The ratio of hypotenuse to short leg is φ; the ratio of long leg to short leg is √φ ≈ 1.272. The reciprocal of √φ is φ−1/2 ≈ 0.786. - Plimpton 322: Old Babylonian tablet (c. 1800 BCE) lists 15 rows of Pythagorean triples in sexagesimal (base-60). The standard reconstruction uses p, q coprime integers with p>q, generating triples (p2 − q2, 2pq, p2 + q2). The tablet's column of "diagonal" ratios corresponds to \(\sec^2\theta\
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Related
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BibTeX
@misc{caldin2026kepler,
title = {{Kepler Triangle and Plimpton 322: No Direct Evidence Linking √φ to 0.786 — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23658305},
url = {https://zenodo.org/records/23658305},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Kepler Triangle and Plimpton 322: No Direct Evidence Linking √φ to 0.786 — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/26
PB - Zenodo
DO - 10.5281/zenodo.23658305
UR - https://zenodo.org/records/23658305
AB - FINDING: The search results are mostly video titles and abstracts, not substantive mathematical analyses. The core mathematical content is implicit: the Kepler triangle (sides 1, √φ, φ) and Plimpton 322 (Babylonian Pythagorean triples in base-60). No direct evidence links √φ (1.272) to 0.786 (which is √φ/φ = φ⁻¹/² ≈ 0.786) in the provided text. MATH: - Kepler triangle: right triangle with sides 1 : √φ : φ, where φ = (1+√5)/2 ≈ 1.618. The ratio of hypotenuse to short leg is φ; the ratio of long leg to short leg is √φ ≈ 1.272. The reciprocal of √φ is φ^−1/2 ≈ 0.786. - Plimpton 322: Old Babylonian tablet (c. 1800 BCE) lists 15 rows of Pythagorean triples in sexagesimal (base-60). The standard reconstruction uses p, q coprime integers with p>q, generating triples (p^2 − q^2, 2pq, p^2 + q^2). The tablet's column of "diagonal" ratios corresponds to \(\sec^2\theta\ Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -