3700-year-old Babylonian clay tablet contains the world's first trigonometry table

Babylonians beat Greeks by 1,000 years in trigonometry Study

The ancient city of Babylon came into existence during Mesopotamia civilization and became famous for its awesome Hanging Gardens.

Up until fairly recently, researchers were not quite sure what its goal was.

Dr. Mansfield read about Plimpton 322 by chance when preparing material for first year mathematics students at UNSW.

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, ' said Mansfield. The hypothesis is "mathematically robust, but for the time being, it is highly speculative", she says.

Ancient Greek Hipparchus has been dubbed "the father of trigonometry" and was widely believed to have created the first trigonometric table.

Pythagorean triples are sets of numbers that correspond to the sides of right triangles. The study authors expanded on prior research suggesting that Plimpton 322 was broken and incomplete, and they determined that there were originally six columns of figures on the tablet.




Daniel Mansfield, of the university's school of mathematics and statistics, described the tablet which may unlock some of their methods as "a fascinating mathematical work that demonstrates undoubted genius" - with potential modern application because the base 60 used in calculations by the Babylonians permitted many more accurate fractions than the contemporary base 10.

Banks was hunting for the fabled Ark of the Covenant, which was brought to Jerusalem by King David around 1000 BC but disappeared when the city was destroyed by the Babylonians in 587 BC, prompting multiple theories about its fate.

Daniel Mansfield holds the 3700-year-old Babylonian tablet that he and colleagues used to make their case. One huge advantage of this is that you don't have to do as much rounding up.

Plimpton 322 (P322) is one of the most sophisticated scientific artifacts of the ancient world, containing 15 rows of arithmetically complicated Pythagorean triples.

"This means it has great relevance for our modern world". But the Guardian reports Babylonian mathematicians may have gotten there 1,000 years earlier. The "Babylon - Myth and Truth" exhibition in Berlin on July 23, 2008.

NSW researchers Dr Daniel Mansfield and professor Norman Wildberger say the identification of a pattern called "Pythagorean triples" was a key clue to pinpointing the tablet's goal. This opens up numerous possibilities in the future, especially as only a small percentage of the other tablets in existence have been seriously studied.

If the new interpretation is right, P322 would not only contain the earliest evidence of trigonometry, but it would also represent an exact form of the mathematical discipline, rather than the approximations that estimated numerical values for sines and cosines provide, notes Mathieu Ossendrijver, a historian of ancient science at Humboldt University in Berlin.

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