Babylonians beat Greeks by 1,000 years in trigonometry: Study

Sydney : Babylonians were the pioneers of trigonometry -- the study of triangles -- and they trumped the Greeks by 1,000 years, revealed an analysis of a 3,700-year-old mathematical clay tablet, whose purpose was not known till now.

The findings showed that the Babylonian clay tablet, discovered in the early 1900s in southern Iraq, is the world's oldest and most accurate trigonometric table, possibly used by ancient mathematical scribes to calculate how to construct palaces and temples and build canals.

Known as Plimpton 322, the small tablet has four columns and 15 rows of numbers written on it in the cuneiform script of the time using a base 60, or sexagesimal, system.

"Plimpton 322 was a powerful tool that could have been used for surveying fields or making architectural calculations to build palaces, temples or step pyramids," said Daniel Mansfield, scientists at the University of New South Wales in Australia. 

Until now, the widely accepted view was that the tablet was a teacher's aid for checking students' solutions of quadratic problems.

"The huge mystery, until now, was its purpose -- why the ancient scribes carried out the complex task of generating and sorting the numbers on the tablet," Mansfield said. 

"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. It is a fascinating mathematical work that demonstrates undoubted genius," he said in the paper published in the journal Historia Mathematica.

Hipparchus -- the Greek astronomer, who lived in about 120 BC -- was long been regarded as the father of trigonometry. His "table of chords" on a circle was considered as the oldest trigonometric table.

But "Plimpton 322 predates Hipparchus by more than 1,000 years," said Norman Wildberger, Associate Professor, UNSW. 

Further, the 15 rows on the tablet were deciphered as a sequence of 15 right-angle triangles, which are steadily decreasing in inclination.

The researchers also demonstrated how the ancient scribes, who used a base 60 numerical arithmetic similar to our time clock, rather than the base 10 number system we use, could have generated the numbers on the tablet using their mathematical techniques.

The tablet, which is thought to have come from the ancient Sumerian city of Larsa, has been dated to between 1822 and 1762 BC. 

"With Plimpton 322 we see a simpler, more accurate trigonometry that has clear advantages over our own," Wildberger noted.