Published: Sat, August 26, 2017
Science | By Nancy Frank

Babylonians, not Greeks, may have been first to study trigonometry

Babylonians, not Greeks, may have been first to study trigonometry

It has four columns and 15 rows of number in modern cuneiform script written in a base 60, or sexagesimal, system, Newsweek reports.

The Greek astronomer Hipparchus, who lived about 120 years BC, has always been regarded as the father of trigonometry, with his "table of chords" on a circle considered the oldest trigonometric table.

Trigonometry is a subject that haunts many students in their mathematics class, but a new study carried out by researchers from the University of New South Wales (UNSW) in Australia suggests that ancient Babylonians developed a far superior and advanced form of trigonometry about 3,700 years back.

"Plimpton 322 has puzzled mathematicians for more than 70 years, since it was realised it contains a special pattern of numbers called Pythagorean triples", Dr Daniel Mansfield of the School of Mathematics and Statistics in the UNSW Faculty of Science said in a statement. With this, they reckon, scribes using a base 60 numerical arithmetic similar to our time clock, could have generated the numbers on the tablet.

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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. Whilst, Dr Mansfield relays with more than a hint of dismay, "Babylonian mathematics may have been out of fashion for more than 3000 years", the trigonometric table in question could have applications in modern industries like surveying, education, and computer graphics.

Plimpton 322-now the world's oldest known trigonometry table. Analysis of the tablet showed that the ancient Babylonians knew about the Pythagorian Theorem long before the rise of ancient Greece, but the tablet's exact goal remained a mystery. The left-hand edge of the tablet, however, is broken, although scientists built on previous research to present new mathematical evidence that there were originally six columns and the tablet was meant to be completed with 38 rows.

One of the stronger theories was that it was a teaching aid for checking quadratic problems, but new research conducted by UNSW scientists Daniel Mansfield and Norman Wildberger now confirms the markings on the tablet as a trigonometry table.

For almost 100 years, the mysterious tablet has been referred to as Plimpton 322.

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"It is a fascinating mathematical work that demonstrates undoubted genius", he said.

He and Dr. Wildberger made a decision to study Babylonian mathematics and examine the different historical interpretations of the tablet's meaning.

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

Generations of schoolchildren have learned that Ancient Greek thinkers invented trigonometry - but rows of numbers deciphered on an ancient stone tablet have turned that idea upside down.

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From what remains, the researchers have dubbed it one of the most accurate trigonometric tables ever, thanks to its reliance on ratio-based measurements instead of angles, but others aren't convinced. "The mathematical world is only waking up to the fact that this ancient but very sophisticated mathematical culture has much to teach us", Wildberger said.

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