Bisection of Trapezoids in Elamite Mathematics

TL;DR

This paper investigates a unique Elamite mathematical problem involving trapezoid bisection, highlighting its differences from Babylonian methods and exploring its underlying mathematical ideas and innovative approach.

Contribution

It presents the first analysis of a distinct Elamite trapezoid bisection problem, contrasting it with Babylonian techniques and proposing possible mathematical concepts behind it.

Findings

The problem differs from Babylonian trapezoid bisection methods.

Identifies potential mathematical ideas in the Elamite problem.

Suggests an innovative approach in Elamite mathematics.

Abstract

The bisection of trapezoids by transversal lines has many examples in Babylonian mathematics. In this article, we study a similar problem in Elamite mathematics, inscribed on a clay tablet held in the collection of the Louvre Museum and thought to date from between 1894--1595 BC. We seek to demonstrate that this problem is different from typical Babylonian problems about bisecting trapezoids by transversal lines. We also identify some of the possible mathematical ideas underlying this problem and the innovative approach that might have motivated its design.