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3700-year-old Babylonian tablet 'solved', revealing true birth of trigonometry

3700-year-old Babylonian tablet 'solved', revealing true birth of trigonometry

It was not clear why the scribes had performed the complex task of generating and sorting the numbers on the tablet, according to Mansfield.

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.

"The ancient Mesopotamians built largely out of clay and mud, so their structures didn't last that long", Wildberger said, adding that there were a few exceptions, "the most notable being the Ziggurat of Ur, which is still around - it was restored by later kings and also by Saddam Hussein - and dates from before the old Babylonian period".

Discovered by 20th century archaeologist Edgar Banks, the ancient clay fragment, known as Plimpton 322, has puzzled scientists for decades.

The tablet is arranged in a series of 15 rows intersected by four columns.

"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", Mansfield said.

Mansfield read about Plimpton 322 by chance and chose to study Babylonian mathematics after realising that it had parallels with the rational trigonometry of Wildberger's book Divine Proportions: Rational Trigonometry to Universal Geometry.

The researchers believe that modern mathematics has a lot to learn from the simplicity and accuracy of Babylonian trigonometry. 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 objective remained a mystery.

The Greek astronomer Hipparchus has widely been considered the father of trigonometry.

"We also demonstrate how the ancient scribes, who used a base 60 numerical arithmetic similar to our time clock, rather than the base 10 number system we use, could have generated the numbers on the tablet using their mathematical techniques".

'A treasure-trove of Babylonian tablets exists, but only a fraction of them have been studied yet. Descending down the tablet, the ratios decrease the triangle's inclination, creating narrower triangles.

Building on previous research, Mansfield and Wildberger were able to show that two columns and 23 rows are missing-the original tablet contained six columns and 38 rows.

Plimpton 322 is inscribed with sequences of Pythagorean triples, sets of three positive whole numbers that follow the mathematical rules for right-angle triangles.

Mansfield described the tablet in a video posted on the university's YouTube channel, featured above. "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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