Scientists at the University of New South Wales, in Australia, have recently analyzed a 3700-year old Babylonian clay tablet, arguing that its purpose may have been to dictate what they now believe to be the world’s oldest—and, more importantly, most accurate—trigonemtric table in history. Experts speculate that this tablet might have helped ancient mathematicians calculate how to build the temples and palaces—and even canals—we have long since uncovered.
Essentially, then, this new research contradicts the standing theory that it was the Greeks who first studied and used trigonometry (that is the study of triangles) to reveal far more sophisticated ancient mathematical processing than we have known.
The small tablet—which is known as Plimpton 322—was actually originally discovered in the early 20th century. While the tablet, itself, is pretty well preserved, we don’t know how many rows and columns it had housed, in total, when it was a functioning math tool. Thus it is difficult to determine its exact purpose (if it had a specific one, at all). Some researchers theorize the numbers on the tablet were used as a teaching tool that helped mathematics students check their work. Some say, perhaps, it was simply a way to help solve algebra problems but, in this case, only analyzed Pythagorean triples.
The tablet—as we know it today—consists of six columns and 38 rows. Analysts argue that if the tablet were still complete, it might have also featured common trigonometric ratios, which the reader could have then used to calculate unknown angles in a method that is actually more accurate than what we use today with modern trigonometry.
Study co-author David Mansfield comments, “Our research reveals that Plimpton 322 describes the shapes of right-angle triangles using a novel kind of trigonometry based on ratios, not angles and circles. It is a fascinating mathematical work that demonstrates undoubted genius.”
He goes on to say, “The tablet not only contains the world’s oldest trigonometric table; it is also the only completely accurate trigonometric table, because of the very different Babylonian approach to arithmetic and geometry. The huge mystery, until now, was [Plimpton 332’s] purpose—why the ancient scribes carried out the complex task of generating and sorting the numbers on the tablet,” adding that it “not only contains the world’s oldest trigonometric table; it is also the only completely accurate trigonometric table, because of the very different Babylonian approach to arithmetic and geometry.”