Monday, August 28, 2017 by Frances Bloomfield
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.”
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