Babylonian tablet shows Greeks not 1st to invent trigonometry

The tablet was possibly used by ancient mathematical scribes to calculate how to construct palaces and temples and build canals using trigonometry - the study of triangles, researchers said.

Published On: Aug 26, 2017 02:28 PM IST | Updated On: Aug 26, 2017 04:58 AM IST |   133

Greeks were not the first to invent trigonometry, say scientists who found that a famous 3,700-year old Babylonian clay tablet is the world's oldest and most accurate trigonometric table.

The tablet was possibly used by ancient mathematical scribes to calculate how to construct palaces and temples and build canals using trigonometry - the study of triangles, researchers said.

Known as Plimpton 322, the small tablet was discovered in the early 1900s in what is now southern Iraq by archaeologist Edgar Banks, the person on whom the fictional character Indiana Jones was based.

It has four columns and 15 rows of numbers written on it in the cuneiform script of the time using a base 60, or sexagesimal, system.

Scientists at the University of New South Wales in Australia provide an alternative to the widely-accepted view that the tablet was a teacher's aid for checking students' solutions of quadratic problems.

"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," researchers said.

"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," they said.

"It is a fascinating mathematical work that demonstrates undoubted genius," they added.

A trigonometric table allows you to use one known ratio of the sides of a right-angle triangle to determine the other two unknown ratios.

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

"Plimpton 322 predates Hipparchus by more than 1,000 years," said Norman Wildberger, an associate professor at UNSW.

"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," Wildberger said.

"Plimpton 322 was a powerful tool that could have been used for surveying fields or making architectural calculations to build palaces, temples or step pyramids," researchers said.

The tablet, which is thought to have come from the ancient Sumerian city of Larsa, has been dated to between 1822 and 1762 BC.

It is now in the Rare Book and Manuscript Library at Columbia University in New York.

A Pythagorean triple consists of three positive whole numbers such that the sum of the square of two numbers is equal to the square of the third.

The integers 3, 4 and 5 are a well-known example of a Pythagorean triple, but the values on Plimpton 322 are often considerably larger with, for example, the first row referencing the triple 119, 120 and 169.

The name is derived from Pythagoras' theorem of right- angle triangles which states that the square of the hypotenuse (the diagonal side opposite the right angle) is the sum of the squares of the other two sides.

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