An ancient clay tablet from 1800BC proves that the Greeks did not develop trigonometry but rather, it was the Babylonians who established this aspect of mathematics some 1,500 years before Pythagoras got his hands on the triangle and Hipparchus fathered the subject around 120BC with his “table of chords.” This was once considered to be the oldest trigonometric table.
Known as Plimpton 332, the 12.7 cm by 8.8 cm tablet is estimated to be 3,700 years old and was first discovered at the turn of the century in Southern Iraq by Edgar Banks, the American archaeologist and diplomat famed for being the muse behind Indiana Jones. He then sold it to G. A Plimpton in 1922. Hence its namesake. It was thought to have originally come from the ancient Sumerian City of Larsa.
Its true meaning has confused researchers and scientists since then, until Dr. Daniel Mansfield and N.J. Wildberger at the University of New South Wales, Australia discovered its purpose as the world’s oldest and most accurate trigonometric table.
In their study published in Historia Mathematica and titled “Plimpton 322 is Babylonian exact sexagesimal trigonometry," the scientists describe how the table was written out and understood.
“The obverse (front) is divided by three vertical lines into four columns, each with a heading, the first of which is partially obscured by damage, while the others are clearly readable. The main body of the obverse is ruled by neat horizontal lines into fifteen equally spaced rows containing sexagesimal numbers, some of which are quite large. The vertical lines continue on the bottom and reverse, which are otherwise empty.”
The differences in the tablet’s trigonometric formula as compared to today’s practices are startling. Firstly, modern trigonometry uses the base number of 10 resulting in the need for angles and approximations, whereas the Babylonians established a base number of 60. They used it in the way we tell time today. Experts muse that because 60 is easier to divide by 3, it provided far more accurate calculations in applications such as constructing temples, canals, step pyramids and canals.
“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,” claims Dr. Daniel Mansfield of the School of Mathematics and Statistics in the UNSW Faculty of Science.
Mansfield and Wildberger believe that the formulas pulled from the tablet can be incorporated into modern system’s such as: surveying, computers and education.
“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.” Wildeberger told The Telegraph.
The tablet is currently housed in in the Rare Book and Manuscript Library at Columbia University in New York.