Babylonians Used Applied Geometry 1,000 Years Before Pythagoras

Calculations inscribed on a clay tablet helped ancient people document property boundaries, new research suggests

“With this new tablet, we can actually see for the first time why they were interested in geometry: to lay down precise land boundaries,” says researcher Daniel Mansfield. UNSW Sydney

Markings on a clay tablet made in Babylon between 1900 and 1600 B.C.E. are the oldest known evidence of humans using applied geometry, a new analysis finds. As Michelle Starr reports for Science Alert, officials in the Old Babylonian period used the artifact, known as Si.427, to delineate land boundaries.

“In this case, it tells us legal and geometric details about a field that’s split after some of it was sold off,” says Daniel Mansfield, a mathematician at the University of New South Wales (UNSW) in Australia, in a statement. Mansfield published his findings in the journal Foundations of Science this week.

Si.427 uses number sets now known as Pythagorean triples to make mathematical calculations based on precise right angles. The ancient Greek philosopher Pythagoras, who developed geometric principles using the mathematical concept, was born in 570 B.C., more than 1,000 years after the tablet’s creation.

“The Greeks invented their trigonometry because they were studying astronomy, but the Babylonians had their own separate variant of trigonometry which they developed to solve problems about land and boundaries,” Mansfield tells Vice’s Becky Ferreira.

One side of the artifact features a diagram showing rectangular fields with opposite sides of equal length, writes Donna Lu for the Guardian. The other contains a description of the land—including marshy areas, a threshing floor and a nearby tower—in cuneiform script.

“Much like we would today, you’ve got private individuals trying to figure out where their land boundaries are,” Mansfield says to the Guardian, “And the surveyor comes out but instead of using a piece of GPS equipment, they use Pythagorean triples.”

Mansfield and fellow UNSW mathematician Norman Wildberger previously found evidence that a different Old Babylonian tablet known as Plimpton 322 contained the earliest known representation of Pythagorean triples.

As Carl Engelking reported for Discover magazine in 2017, the pair argued that Babylonians used a base-60 system to make calculations based on the lengths of the sides of a right triangle. At the time, however, the researchers didn’t know what the calculations were used for. They speculated that the measurements could have been employed in construction of canals, palaces and temples, or perhaps in land surveying.

The tablet uses Pythagorean triples to draw precise land boundaries. UNSW Sydney

The key to the puzzle proved to be Si.427, a tablet discovered in 1894 in what’s now Iraq. Mansfield found the clay artifact at the Istanbul Archaeology Museums, where it had been housed for decades, largely overlooked, as he explains for the Conversation.

“With this new tablet, we can actually see for the first time why they were interested in geometry: to lay down precise land boundaries,” says Mansfield in the statement. “This is from a period where land is starting to become private—people started thinking about land in terms of ‘my land and your land,’ wanting to establish a proper boundary to have positive neighborly relationships.”

Other tablets from the period help flesh out the ways that people addressed issues surrounding land ownership. A number of them refer to a person named Sin-bel-apli. One describes a dispute between Sin-bel-apli and a wealthy female landowner.

“The dispute is over valuable date palms on the border between their two properties,” Mansfield says in the statement. “The local administrator agrees to send out a surveyor to resolve the dispute. It is easy to see how accuracy was important in resolving disputes between such powerful individuals.”