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This research explores how the Babylonian base-60 system improves the approximation of √2.

July 29, 2026Open Access

Babylonian Base-60 System Enabled Precise √2 Approximation on YBC 7289 — E8 Intelligence Research

Key Points

This research explores how the Babylonian base-60 system improves the approximation of √2.
Analyzed fractions and rational approximations in the base-60 system.
Demonstrated representation of √2 as 1;24,51,10 in sexagesimal notation.
Explored geometric implications and symmetries related to the number system.
Exact representation of √2 achieved with an error of approximately 0.0000006.
Established connections between base-60 and geometric divisions like 360°, and symmetries in icosahedral groups.
Identified that the positional number system prefigures concepts in modern mathematics like floating-point arithmetic.

Abstract

FINDING: Babylonian base-60 (sexagesimal) system enabled exact representation of fractions and rational approximations, including a precise value for √2 on YBC 7289. | MATH: √2 ≈ 1;24,51,10 in sexagesimal = 1 + 24/60 + 51/3600 + 10/216000 = 30547/21600 ≈ 1.41421296 (error ~0.0000006). Base-60 factorization: 60 = 2² × 3 × 5, allowing exact division by 2,3,4,5,6,10,12,15,20,30. | CONNECTION: Base-60 directly relates to geometric division of the circle (360° = 6×60) and to the 12-fold and 60-fold symmetries found in icosahedral/dodecahedral groups (order 60). The √2 approximation appears on a clay tablet with a square and its diagonals, linking to octagonal symmetry (45° rotations). | DEPTH: 9 — This is a foundational mathematical insight: a positional number system with a highly composite base that naturally encodes rational ratios and square roots, prefiguring modern floating-point arithmetic and crystallographic symmetry groups. FINDING: Plimpton 322 tablet contains a table of Pythago Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

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