Tablet Reveals Babylonians Studied Trigonometry Before the Greeks

In recent years, there have been all kinds of anthropological breakthroughs radically shifting our ideas of ancient life and the capacities of our prehistory predecessors — from the discovery of the world’s oldest home in South Africa to new evidence that titanium dioxide was utilized in Inca objects some 400 years before its “discovery” in the United States. In the same vein, research performed by scientists at UNSW Sydney has revealed that a famous 3,700-year-old Babylonian clay tablet is inscribed with accurate trigonometry.

The translation on the tablet, called Plimpton 322, was performed by a team including Daniel Mansfield of the School of Mathematics and Statistics in the UNSW Faculty of Science. The analysis of the tablet’s contents, which feature four columns and 15 rows of numbers written in the cuneiform script of the time, has identified the tablet as the world’s oldest and most accurate trigonometry table. It also indicates that the Babylonians, rather than the Greeks, were the first to make a formal mathematical study of triangles. Jump back, Pythagoras!

Plimpton 322, a 3,700 year old Babylonian tablet held in the Rare Book and Manuscript Library at Columbia University in New York.

“Plimpton 322 has puzzled mathematicians for more than 70 years, since it was realised it contains a special pattern of numbers called Pythagorean triples,” said Mansfield in a press release from UNSW.

“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,” continued Mansfield. “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 numeric calculations on the tablet use a base 60, or sexagesimal, system.

A study on the tablet by Mansfield and UNSW Associate Professor Norman Wildberger was published in Historia Mathematica in 2017, and concludes that the Babylonians discovered exact sexagesimal trigonometry at least 1,500 years before the ancient Greeks discovered trigonometry. It seems that anthropology and mathematics have teamed up to strike an acute blow for the mathletes of Ancient Babylon!

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