Ancient clay tablet bears the oldest known example of applied geometry
Researchers in Australia have made a discovery that may shake up the history of mathematics, revealing evidence of applied geometry being used for the purposes of land surveying some 3,700 years ago. Found on a Babylonian clay tablet discovered in the late 19th century, the detailed etchings are believed to represent the oldest known example of applied geometry, and feature mathematical techniques linked to the Greek philosopher Pythagoras that were well ahead of their time.
The discovery centers on a clay tablet known as Si.427, which has been on display in an Istanbul museum since being discovered in what is now central Iraq in 1894. Dr Daniel Mansfield from the University of New South Wales was moved to study the specimen after previous work on another artifact from the same period, between 1900 and 1600 B.C.E,. appeared to show early evidence of the use of trigonometry.
“It is generally accepted that trigonometry – the branch of maths that is concerned with the study of triangles – was developed by the ancient Greeks studying the night sky in the second century B.C.E.,” says Dr Mansfield. “But the Babylonians developed their own ‘proto-trigonometry’ to solve problems measuring the ground, not the sky.”
Mansfield and his fellow researchers suspected the artifact, called Plimptom 322, had some sort of practical use, such as the construction of palaces or the surveying of fields. When sifting through literature on the topic, Mansfield then learned of Si.427 and its peculiar etchings and tracked down the location of the tablet, leading him to the Archaeological Museum in Istanbul.
"Even after locating the object it still took months to fully understand just how significant it is, and so it's really satisfying to finally be able to share that story," he says.
Created by an Old Babylonian land surveyor who wrote on it with a stylus, the clay tablet Si.427 features a diagram of a field being split up for sale. And it is the accuracy of the boundaries that really piqued the interest of Mansfield and his team, who say the level of precision was achieved with the use of what are known as Pythagorean triples, a mathematical technique used to create the perfect right angle.
“It’s the only known example of a cadastral document from the Old Babylonian period, which is a plan used by surveyors to define land boundaries," says Mansfield. "In this case, it tells us legal and geometric details about a field that’s split after some of it was sold off.”
According to the researchers, the tablet tells a broader tale about why the Old Babylonians become interested in geometry, coinciding with a time when private land ownership was becoming more common and proper and fair boundaries needed to be established. There are still some mysteries to unravel around Si.427, such as the meaning of a set of numbers "25,29" on the back, but there is no doubting its significance.
“The discovery and analysis of the tablet have important implications for the history of mathematics,” Dr Mansfield says. “For instance, this is over a thousand years before Pythagoras was born.”
The research was published in the journal Foundations of Science, while you can hear from Mansfield in the video below.
Source: University of New South Wales