Published: Sat, August 26, 2017
Sci-tech | By Jackie Newman

Ancient Tablet May Contain Trigonometric Secrets

Ancient Tablet May Contain Trigonometric Secrets

Consisting of four columns, the palm-sized ancestor to the familiar Sine, Cosine and Tangent trigonometry functions displays 15 rows of inscribed numbers and uses a sexagesimal numeral system. Hipparchus, a Greek mathematician and astronomer whose work dates to between 160 and 120 BC, is credited as the father of trigonometry, but a almost 4,000-year-old stone tablet may be about to totally rewrite the history books.

The tablet contains information written in cuneiform, the language of the Babylonians, who lived in what is nowadays called Iraq in around 2,000 BC. With this, they reckon, scribes using a base 60 numerical arithmetic similar to our time clock, could have generated the numbers on the tablet.

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

The Plimpton 322 tablet is now housed in Columbia University's Rare Book and Manuscript Library in NY.

"We trace the origins of trigonometry to the Old Babylonian era, between the 19th and 16th centuries B.C.E", the paper explains.

"It is a fascinating mathematical work that demonstrates undoubted genius", said University of New South Wales researcher Daniel Mansfield in a press release.

"Bottom line is this: If interpreted as a trig table, it would be the oldest known".

Scientists say they have cracked the secrets of a 3,700-year-old broken clay tablet in the collections of Columbia University.

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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.

By applying Babylonian mathematical models, the researchers were able to show that the tablet would originally have had 6 columns and 38 rows.

Relationships between numbers in the completed table would have represented a novel type of trigonometry - one that relied on ratios instead of angles and circles, according to the study.

Wildberger said: 'It opens up new possibilities not just for modern mathematics research, but also for mathematics education.

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. Dr Daniel Mansfield of the School of Mathematics and Statistics at UNSW attested to this benefit.

He and Dr. Wildberger chose to study Babylonian mathematics and examine the different historical interpretations of the tablet's meaning.

"The huge mystery, until now, was its goal - why the ancient scribes carried out the complex task of generating and sorting the numbers on the tablet". "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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