# This Babylonian Tablet Possibly Contains The First Evidence Of Trigonometry

Posted: Aug 25 2017, 7:26am CDT | by , Updated: Aug 25 2017, 7:28am CDT, in News | Latest Science News

The image of ancient Babylonian tablet, Plimpton 322. Credit: UNSW

## The ancient tablet may represent the oldest and most accurate trigonometric table yet discovered

A 3,700-year old Babylonian clay tablet with mathematical work has been identified as the world's oldest evidence of trigonometry. It suggests that Greeks were not the first to understand the study of triangles. Instead, Babylonians used trigonometry far earlier than previously thought. The finding pushes back the date for the first evidence of trigonometry to more than 1000 years.

"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,” said Dr Daniel Mansfield from University of New South Wales, Australia.

"This means it has great relevance for our modern world. Babylonian mathematics may have been out of fashion for more than 3000 years, but it has possible practical applications in surveying, computer graphics and education. This is a rare example of the ancient world teaching us something new.”

The small tablet, known as Plimpton 322, was discovered in the early 1900s in what is now southern Iraq. Discoverer Edgar Banks the person the character Indiana Jones is loosely based on later sold the artifact to New York publisher George Arthur Plimpton in 1922 and it has been called the Plimpton 322 tablet ever since.

The tablet consists of four columns and 15 rows of numbers inscribed in ancient cuneiform script. It had a base number of 60 instead of base 10 number system we use today and involved the exact ratios of the lengths of the sides of right triangles, rather than angles.

Since its discovery, researchers have been working to determine the purpose of the ancient table. But up to now it was not clearly known.

“Plimpton 322 has puzzled mathematicians for more than 70 years, since it was realized it contains a special pattern of numbers called Pythagorean triples,” said Dr Mansfield.

“The huge mystery, until now, was its purpose – why the ancient scribes carried out the complex task of generating and sorting the numbers on the tablet. Our research reveals that Plimpton 322 describes the shapes of right-angle triangles using a novel kind of trigonometry based on ratios, not angles and circles. It is a fascinating mathematical work that demonstrates undoubted genius.”

UNSW researchers also suggest that the method was possibly used to survey fields and to construct palaces, temples and pyramids. To understand its true meaning, researchers studied Babylonian mathematics and examine the different historical interpretations of the tablets. They found that15 rows on the tablet, forming a sequence of 15 right-angle triangles, are steadily decreasing in inclination. Though the tablet is broken, researchers believe it originally contained 6 columns and should have 38 rows.

If the new interpretation is correct, Plimpton 322 would not only contain the oldest evidence of trigonometry but it also represents the most accurate trigonometric table in the world.

“It opens up new possibilities not just for modern mathematics research, but also for mathematics education. With Plimpton 322 we see a simpler, more accurate trigonometry that has clear advantages over our own,” said study co-author Norman Wildberger.

“A treasure-trove of Babylonian tablets exists, but only a fraction of them have been studied yet. 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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The latest discoveries in science are the passion of Hira Bashir (). With years of experience, she is able to spot the most interesting new achievements of scientists around the world and cover them in easy to understand reporting.