Ancient Clay Tablet Holds Modern-Day Mathematics Applications

Ancient Babylonian Tablet Identified as the World's Oldest Trigonometry Table

Prior to this, it was the Greek astronomer Hipparchus (who lived about 120 years BC) that was credited as the father of trigonometry.

So how did the tablet help Babylonians do their sums?

It also reveals the Babylonians, not the Greeks, were the first to study trigonometry - the study of triangles - and opens up new possibilities for modern mathematics research and education.

The evidence is inscribed on a 3,700-year-old clay tablet known as Plimpton 322 - which was found by an archaeologist and antiques dealer who is said to have inspired Indiana Jones. The tablet's rows describe a sequence of 15 right-angle triangles, decreasing in inclination.

Plimpton 322, a 3,700-year-old Babylonian tablet held in the Rare Book and Manuscript Library at Columbia University in NY.

They now believe the tablet displays the world's oldest and most accurate trigonometric table.

About 70 years ago, researchers determined that the notations on the tablet represented a special numerical pattern known as Pythagorean triples, a grouping of three positive integers, study co-author David Mansfield, a researcher with the School of Mathematics and Statistics at the University of New South Wales in Sydney, said in a statement. The vertical lines continue on the bottom and reverse, which are otherwise empty.

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Said Daniel Mansfield: "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 Sydney researchers describe the Babylonian system as a "novel kind of trigonometry" that is based on ratios instead of angles and circles.

The UNSW Sydney, whose scientists discovered the objective of the tablet, said the left-hand edge of the tablet is broken and the researchers build on previous research to present new mathematical evidence that there were originally six columns and that the tablet was meant to be completed with 38 rows. Lovers of Ancient Greece, in the meantime, will be dismayed to realise that trigonometry, hitherto attributed to the Greeks, actually emerged 1,500 years prior to their society, in Babylonia. An alternate theory had been that it was a teacher's aid used to check students' solutions to quadratic equations.

For almost 100 years, the mysterious tablet has been referred to as Plimpton 322.

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. "With Plimpton 322 we see a simpler, more accurate trigonometry that has clear advantages over our own", Dr. Wildberger said.

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.

"It's rare that the ancient world teaches us something new".

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