(CN) — A 3,700-year-old clay tablet contains a curious list of Pythagorean angles and a math problem scholars have been trying to solve for more than a century. Now, in an analysis published in Foundations of Science on Wednesday, an Australian mathematician argues the Mesopotamian scribe who carved it was calculating rectangles, not triangles.
“We have presented a new interpretation of Plimpton 322 as a table of rectangles that shows which sides are regular and which are not,” explained Daniel Mansfield, professor at the School of Mathematics and Statistics at the University of New South Wales in Sydney, in the paper.
“What was the purpose of the text? Answers to this question are both speculative and necessary. Speculative because the text itself does not provide an answer, and necessary because any interpretation must fit within the wider context of Mesopotamian mathematics,” Mansfield wrote.
Bought by George Plimpton around 1922, the cuneiform tablet was donated to Columbia University in 1936. In 1945, Austrian-American mathematician Otto Neugebauer realized the numbers listed out diagonal triples, leading scholars around the world to ponder their meaning well into the next century.
One thousand years after the cuneiform tablet was created, and 2,500 years before present day, the Greek thinker Pythagoras would develop his eponymous theorem foundational to Euclidean geometry: A2+ B2= C2. Holding true to any right triangle, the principle observes that the size of the longest side multiplied by itself equals the sum of the two smaller sides, each multiplied by themselves.
But why would a scribe need this calculation in ancient Mesopotamia — and how did said individual generate it?
While Plimpton 322 depicts a curious deviation, clay multiplication tables were commonly carved out by scribes trained to memorize mathematical equations, and then distributed to the administrators and engineers who needed them.
Others have theorized that Plimpton 322 represented a theoretical exercise or a form of mathematics completely lost to modern man. British ancient Middle Eastern history scholar Elanor Robson suggested in a 2002 paper the list came from a classroom and may "have enabled a teacher to set his students repeated exercises on the same mathematical problem, and to check their intermediate and final answers without repeating the calculations himself."
With a fresh look at the numbers, Mansfield found not triangles but rectangles depicted in the clay, a calculation he now argues would have been important for surveying land.
In the paper, Mansfield points to the clay tablet Si.427 discovered by Frenchman Vincent Scheil in modern day Iraq in 1894 as an example of rectangular plots of land. Tablet Si.427 is believed to depict the boundaries between Sin-bel-apli, a prominent individual in the community, and an unnamed wealthy female landowner with whom he was in dispute.
The calculation cheat sheet depicted on Plimpton 322 would have allowed a surveyor to accurately measure the boundaries between properties. With all of these pieces to this ancient puzzle in place, Mansfield calls Si.427 the oldest known example of applied geometry in the world.
“I can’t stress how important these tablets are, both mathematically and historically,” Mansfield said in a video released with the paper. “They represent the practical application and theoretical understanding of geometry that was massively advanced for the time, which makes me wonder what other discoveries are out there hiding in plain sight?”
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