Ancient Babylonian clay tablet discovered to be a trigonometry reference sheet for building temples and canals

The 70-year old mystery behind an ancient clay tablet may have finally been solved. Two mathematicians from the University of New South Wales, Australia claim that the tablet known as Plimpton 322 contains the world’s oldest and most accurate trigonometric table. Its purpose, they surmise, was as an aid in the construction of temples, palaces, and canals. Perhaps what’s most remarkable about this new theory is that it could very well rewrite history.

According to Daniel F. Mansfield and Norman Wildberger, Plimpton 322 displays a keen understanding of mathematics. The three-inch-tall, five-inch-wide tablet contains 15 rows and four columns of cuneiform numbers, meaning that it uses a base 60 or sexagesimal numeral system. The 15 rows on the tablet show a sequence of 15 right-angle triangles decreasing in inclination. Mansfield and Wildberger believe that this is because the tablet utilizes ratio-based trigonometry instead of trigonometry derived from angles or circles. Through this, anyone who uses the tablet would be able to determine two unknown ratios of a right-side triangle based off the single known ratio.

Mansfield has described Plimpton 322 as a “fascinating mathematical work that demonstrates undoubted genius.” What was once believed to be a simple teaching aid is in fact something more.

The base-60 system allows the use of whole numbers, resulting in exact calculations in lieu of approximations. Mansfield added that the mathematics on the tablet are more advanced than even modern trigonometry. This, in turn, shows that the Babylonians were the first to study trigonometry and not the ancient Greeks, and that they proved the Pythagorean theorem a thousand years before the famed Greek mathematician Pythagoras was even born. (Related: Bringing back the hanging gardens of Babylon — Indoor urban vertical farming; the next gardening venture for survival and the new agriculture.)

Moreover, Plimpton 322 came before Hipparchus, a Greek astronomer regarded as the father of trigonometry. “Plimpton 322 predates Hipparchus by more than 1000 years. It opens up new possibilities not just for modern mathematics research, but also for mathematics education. With Plimpton 322 we see a simpler, more accurate trigonometry that has clear advantages over our own,” explained Wildberger.

He added: “A treasure-trove of Babylonian tablets exists, but only a fraction of them have been studied yet. The mathematical world is only waking up to the fact that this ancient but very sophisticated mathematical culture has much to teach us.”

Fast facts on Plimpton 322

• Plimpton 322 is part of the George Arthur Plimpton collection at Columbia University, hence its name. The American philanthropist and publisher George Arthur Plimpton was an avid collector of books and manuscripts that documented the history of education. Plimpton purchased the tablet from Edgar J. Banks in either 1922 or 1923. The collection itself was gifted to the university shortly before Plimpton’s death in 1936.
• Banks, an American archaeologist and diplomat, discovered Plimpton 322 in a location close to the ancient city of Larsa, or modern Tell as-Senkereh, in Iraq.
• According to Oriental scholar Eleanor Robson, it’s highly likely that Plimpton 322 was created 60 years before Larsa fell in 1762 BCE to Hammurabi, the sixth king of the First Babylonian dynasty.
• Plimpton 322 is believed to have had originally six columns and 38 rows. The left-hand edge is missing, however. Robson has postulated that it may be due to Banks removing a chunk of the tablet that was unrelated to the rest of its content.

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Sources include:

ScienceDaily.com
ScienceDirect.com
AMS.org