Babylonians beat Greeks by 1000 years in trigonometry

Posted August 26, 2017

About 70 years ago, researchers determined that the notations on the tablet represented a special numerical pattern known as Pythagorean triples, a grouping of three positive integers, study co-author David Mansfield, a researcher with the School of Mathematics and Statistics at the University of New South Wales in Sydney, said in a statement.

Said Wildberger: "Plimpton 322 predates Hipparchus by more than 1,000 years".

This Babylonian tablet, known as Plimpton 322, is the world's oldest-and most accurate-trigonometric table, according to research published this week in Historia Mathematica.

"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", says one of the researchers, Daniel Mansfield.

Researchers at the University of New South Wales in Sydney, Australia say they have discovered just that by studying the goal of a famous 3,700-year old Babylonian clay tablet called Plimpton 322, which they believe is actually the world's oldest and most accurate trigonometric table. "With Plimpton 322 we see a simpler, more accurate trigonometry that has clear advantages over our own", Dr. Wildberger said.

The tablet, thought to have come from the ancient Sumerian city of Larsa, has been dated to between 1822 and 1762 BC and is housed in the Rare Book and Manuscript Library at Columbia University, New York.

The main body of the obverse is ruled by neat horizontal lines into 15 equally spaced rows containing sexagesimal (base 60) numbers, some of which are quite large. An alternate theory had been that it was a teacher's aid used to check students' solutions to quadratic equations. The ancient Greeks were not the ones to invent the first trigonometric table; the ancient Babylonians were. The tablet's rows describe a sequence of 15 right-angle triangles, decreasing in inclination.

'The huge mystery, until now, was its objective - why the ancient scribes carried out the complex task of generating and sorting the numbers on the tablet'. (Glue residue found on the side suggest the break was recent.) The team used previous research on Plimpton 322 to speculate that it was originally built with six columns and 38 rows.

The tablet contains information written in cuneiform, the language of the Babylonians, who lived in what is nowadays called Iraq in around 2,000 BC.

Those of you who can remember trigonometry can feel free to forget it, because ancient Babylonian mathematicians had a better way of doing it - using base 60! The tablet, known as Plimpton 322, was previously identified as a table filled with sets of Pythagorean triples, but nobody knew its goal was anything more than an educational tool. "The mathematical world is only waking up to the fact that this ancient but very sophisticated mathematical culture has much to teach us".