Base-60 and the 360° Circle: Sexagesimal Math in Mesopotamian Sky Maps — E8 Intelligence Research

FINDING: Sumerian/Assyrian planispheres encode star positions and a possible celestial event, but the mathematical core is the base-60 positional system and the 360° circle division used to map the sky. | MATH: Base-60 (sexagesimal) place-value system; 360° = 6×60; 1° = 60′ (arcminutes), 1′ = 60″ (arcseconds); the tablet's 14 cm diameter implies a scale of ~25.7° per cm (360/14) — a linear angular density; the Nineveh planisphere's cuneiform labels use sexagesimal fractions (e.g., 1/60, 1/3600) for star coordinates. | CONNECTION: The 360° circle is the direct ancestor of the golden-angle approximations: 360° × 0.618 = 222.48° (or its complement 137.52°), and 360° × 0.382 = 137.52° — the golden angle appears in phyllotaxis and spiral structures. The sexagesimal system's divisors (2,3,4,5,6,10,12,15,20,30,60) generate regular polygons and thus crystallographic point groups (2-fold, 3-fold, 4-fold, 6-fold rotational symmetries) — the same symmetries found in hexagonal ice, quartz, and man Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-06
DOI
https://doi.org/10.5281/zenodo.22472080
Primary Topic
Ancient Near East History
Type
preprint
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preprint

Base-60 and the 360° Circle: Sexagesimal Math in Mesopotamian Sky Maps — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Ancient Near East History
preprint

Base-60 and the 360° Circle: Sexagesimal Math in Mesopotamian Sky Maps — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: Sumerian/Assyrian planispheres encode star positions and a possible celestial event, but the mathematical core is the base-60 positional system and the 360° circle division used to map the sky. | MATH: Base-60 (sexagesimal) place-value system; 360° = 6×60; 1° = 60′ (arcminutes), 1′ = 60″ (arcseconds); the tablet's 14 cm diameter implies a scale of ~25.7° per cm (360/14) — a linear angular density; the Nineveh planisphere's cuneiform labels use sexagesimal fractions (e.g., 1/60, 1/3600) for star coordinates. | CONNECTION: The 360° circle is the direct ancestor of the golden-angle approximations: 360° × 0.618 = 222.48° (or its complement 137.52°), and 360° × 0.382 = 137.52° — the golden angle appears in phyllotaxis and spiral structures. The sexagesimal system's divisors (2,3,4,5,6,10,12,15,20,30,60) generate regular polygons and thus crystallographic point groups (2-fold, 3-fold, 4-fold, 6-fold rotational symmetries) — the same symmetries found in hexagonal ice, quartz, and man Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Ancient Near East History
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