Friday, 22 September, 2017

Mathematicians Crack Mystery of Babylonian Clay Tablet 'Plimpton 322'

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Garry Little | 26 August, 2017, 01:14

The ancient tablet consists of 15 rows of numbers with cuneiform writing on it that describe a base of 60, or a sexagesimal system.

The Greek astronomer Hipparchus, who lived about 120 years BC, has always been regarded as the father of trigonometry, with his "table of chords" on a circle considered the oldest trigonometric table.

The tablet was most likely written between 1822-1762 BC (around the time of Hammurabi, the sixth king of the First Babylonian Dynasty).

Babylonians were the pioneers of trigonometry - the study of triangles - and they trumped the Greeks by 1,000 years, revealed an analysis of a 3,700-year-old mathematical clay tablet, whose objective was not known till now.

Thousands of years ago, mathematicians in Babylonia used a base 60 numerical system rather than the base 10 system that forms the foundation of modern arithmetic. Descending down the tablet, the ratios decrease the triangle's inclination, creating narrower triangles.

'Plimpton 322 has puzzled mathematicians for more than 70 years, since it was realised it contains a special pattern of numbers called Pythagorean triples, ' according to Dr Daniel Mansfield of the School of Mathematics and Statistics in the University of New South Wales Faculty of Science. The vertical lines continue on the bottom and reverse, which are otherwise empty. The group's research was published in the journal Historia Mathematica.

Until now. The tablet, it has been discovered, proffers the world's oldest trigonometric table, describing the shape of right-angle triangles based on ratios, as opposed to angles and circles, which is the conventional method.

"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.

Until now, the widely accepted view was that the tablet was a teacher's aid for checking students' solutions of quadratic problems.

You can see Plimpton 322 itself here, where you will also learn that commercial reproduction of images depicting the tablet is forbidden without permission. Though the left edge of the tablet is broken, the researchers believe there were originally 6 columns and that the tablet was meant to be completed with 38 rows.

"It is wonderful that Mr. Mansfield's work with Norman Wildberger is bringing more attention to this treasure of Columbia", explained Jennifer Lee, a curator at Columbia University's Rare Book and Manuscript Library, in a statement emailed to Fox News.

Thus, scribes could use the table to carry out the complex task of generating and sorting the numbers on the tablet; they could take one known ratio of the sides of a right-angle triangle to determine the other two unknown ratios. "The mathematical world is only waking up to the fact that this ancient but very sophisticated mathematical culture has much to teach us".


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