Babylonians developed trigonometry 3700 years back, much earlier than Greeks

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The "Plimpton322" tablet was discovered in the early 1900s in the ancient city of Larsa in what is now southern Iraq by by archaeologist, academic, diplomat and antiquities dealer Edgar Banks, on whom the fictional character Indiana Jones was based. "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".

It turns out this was a historically unfortunate smiting - because if the Babylonians had been able to better communicate their knowledge, mathematics could be 1,000 years more advanced.

The Sydney researchers describe the Babylonian system as a "novel kind of trigonometry" that is based on ratios instead of angles and circles.

Mansfield, who has published his research with his colleague Norman Wildberger in the journal Historia Mathematica, says that while mathematicians understood for decades that the tablet demonstrates that the theorem long predated Pythagoras, there had been no agreement about the intended use of the tablet.

Now researchers from the University of New South Wales are calling it one of the oldest and possibly most accurate trigonometric tables of the ancient world.

Wildberger added: "With Plimpton 322 we see a simpler, more accurate trigonometry that has clear advantages over our own". The tablet is now kept in the Rare Book and Manuscript Library at Columbia University in NY.

They now believe the tablet displays the world's oldest and most accurate trigonometric table.

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

The research provides an alternative theory to the widely-held view that the Plimpton 322 was a teacher's aid for checking students' solutions of quadratic problems.

"A treasure-trove of Babylonian tablets exist, but only a fraction of them have been studied yet". Unlike modern-day trigonometry, Babylonians used a sexagesimal system with base 60 rather than base ten that is used in modern mathematics.

"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". In the 1980s, some researchers suggested that numbers written on Plimpton 322 show that ancient Babylonians had knowledge of trigonometry, but this idea was dismissed at that time.

"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", Mansfield said. 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.

"This is a rare example of the ancient world teaching us something new".

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