The oldest example of $\pi=3+1/8$ in Sumer: Calculation of the area of a circular plot

TL;DR

This paper traces the earliest known use of the formula for the area of a circle, related to +1/8, in Sumerian texts dating back to the 23rd century BCE, revealing ancient mathematical knowledge.

Contribution

It provides historical evidence linking ancient Sumerian calculations to modern circle area formulas, demonstrating early mathematical understanding.

Findings

The formula 0.4,48 times circumference squared was used in Babylonian texts.

Earliest evidence of +1/8 in circle area calculations.

The formula dates back to at least the 23rd century BCE.

Abstract

In this paper I shall show that the formula 0:4,48 times circumference squared for the area of a circle, which occurs in a few Babylonian mathematical texts, can be traced back to at the latest the twenty-third century BCE.