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This research explores the methods used in the YBC 7302 tablet for calculating the area of a circle.

July 21, 2026Open Access

Cuneiform Discovery: YBC 7302 area of circle pi approximation Babylon — E8 Intelligence Research

Key Points

This research explores the methods used in the YBC 7302 tablet for calculating the area of a circle.
Analysis of the YBC 7302 tablet from the Old Babylonian period (c. 1800–1600 BCE)
Examination of the mathematical procedures in Akkadian cuneiform
Application of sexagesimal place-value notation in calculations
The circumference given is C = 60, leading to area calculation through squaring the circumference: 1,0 × 1,0 = 1,0,0 (3,600 in decimal).
The method employed utilizes the reciprocal of 12 to determine the area, reflecting practical surveying techniques.
This approach indicates advanced mathematical concepts present in Babylonian society.

Abstract

**YBC 7302: The Circle Squared by Twelve** **Tablet the circumference *is* the primary datum, reflecting the practical surveyor's reality of measuring a circular field by pacing its perimeter. **Numbers & Calculation:** 1. **Given:** Circumference *C* = 60 (written as **1,0** in sexagesimal place-value notation). 2. **Operation:** Square the circumference: 1,0 × 1,0 = **1,0,0** (3,600 decimal). 3. **Coefficient:** Multiply by the reciprocal of 12 (*igi 12*). Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

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