Australian university scientists solve 3700-year-old mystery

This ancient Babylonian tablet may contain the first evidence of trigonometry

For decades mathematicians have puzzled over the four columns and 15 rows of numbers written on this particular tablet in its cuneiform script.

First we abandon the notion of angle, and instead describe a right triangle in terms of the short side, long side and diagonal of a rectangle. But now, UNSW scientists believe the tablet was used for more practical purposes, such as calculating how to construct palaces, canals and temples. This study's findings hint that these understudied artifacts from a long-dead empire could hold exciting discoveries, not only for understanding the history of mathematics but also for enhancing how math is studied today, Wildberger explained. By examining the evidence with this mindset, and comparing Plimpton 322 with Madhava's table of sines, we demonstrate that Plimpton 322 is a powerful, exact ratio-based trigonometric table.

Researchers at the University of New South Wales in Sydney, Australia say they have discovered just that by studying the objective of a famous 3,700-year old Babylonian clay tablet called Plimpton 322, which they believe is actually the world's oldest and most accurate trigonometric table. Unlike modern-day trigonometry, Babylonians used a sexagesimal system with base 60 rather than base ten that is used in modern mathematics.

The left edge of the tablet is broken, and the Australian researchers reckon that there were originally six columns. Banks sold the tablet to NY publisher George Arthur Plimpton, who later bequeathed it and his collection to Columbia University. But the Guardian reports Babylonian mathematicians may have gotten there 1,000 years earlier. It was not clear why the scribes had performed the complex task of generating and sorting the numbers on the tablet, according to Mansfield.

"The tablet not only contains the world's oldest trigonometric table; it is also the only completely accurate trigonometric table, because of the very different Babylonian approach to arithmetic and geometry", says Dr Daniel Mansfield of the School of Mathematics and Statistics in the UNSW Faculty of Science.

Greek astronomer Hipparchus, who lived in about 120 BC, has always been regarded as the father of the subject.

The researchers believe that modern mathematics has a lot to learn from the simplicity and accuracy of Babylonian trigonometry. "After 3,000 years, Babylonia mathematics might just be coming back into fashion", he said in the video.

The tablet, which is thought to have come from the ancient Sumerian city of Larsa sometime between 1822 and 1762 B.C., is now in the Rare Book and Manuscript Library at Columbia University in NY.

You can see Plimpton 322 itself here, where you will also learn that commercial reproduction of images depicting the tablet is forbidden without permission. Previously, researchers thought that Plimpton 322 might be some sort of teaching aid for the simply geometric equation, but the UNSW Sydney team believes it's much more important.

Scientists at a university in Sydney have solved an ancient mystery that's had mathematicians around the world scratching their heads for more than 70 years.

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