Ancient Iraqis discovered trigonometry 1500 years before Greeks

Hipparchus, a Greek mathematician and astronomer whose work dates to between 160 and 120 BC, is credited as the father of trigonometry, but a almost 4,000-year-old stone tablet may be about to totally rewrite the history books. Similarities in its writing style to that on other Babylonian tablets enabled experts to date it to between 1822 B.C. and 1726 B.C., around the time that King Hammurabi ruled the Babylonian Empire.

It also reveals the Babylonians, not the Greeks, were the first to study trigonometry - the study of triangles - and opens up new possibilities for modern mathematics research and education.

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! Descending down the tablet, the ratios decrease the triangle's inclination, creating narrower triangles.

The Plimpton 322 tablet is now housed in Columbia University's Rare Book and Manuscript Library in NY. He called it the world's oldest and the only completely accurate trigonometric table on record.

"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", Dr. Mansfield added.

Archaeologists have uncovered numerous tablets produced during the time of the Babylonian Empire, but very few of them have been examined in detail.

Its use of ratio-based trigonometry rather than trigonometry based on angles and circles makes it the world's most accurate trigonometric table, Dr Mansfield says. Norman Wildberger, provides an alternative to the widely-accepted view that Plimpton 322 was a scribal school text.

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

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

That's the conclusion of a new paper, Plimpton 322 is Babylonian exact sexagesimal trigonometry, in the new issue of the journal Historia Mathematica.

"The left-hand edge of the tablet is broken and we build on previous research to present new mathematical evidence that there were originally 6 columns and that the tablet was meant to be completed with 38 rows".

"Our research shows that it's a trigonometric table so unfamiliar and advanced that, in some respects, it's superior even to modern trigonometry", he said in the video. 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.

"With Plimpton 322 we see a simpler, more accurate trigonometry that has clear advantages over our own", Wildberger noted. "The mathematical world is only waking up to the fact that this ancient but very sophisticated mathematical culture has much to teach us".

  • Joey Payne