The study of trigonometry or the study of triangles has been widely attributed to the ancient Greeks.
The Greek astronomer Hipparchus, who lived about 120 BC, is broadly considered 鈥渢he father of trigonometry鈥� for compiling the first known 鈥渢able of chords鈥� or trigonometric table, which allows users to figure out the ratio of two sides of a right-angle triangle with only one known ratio.
But what if Hipparchus鈥� table wasn鈥檛 the first and another ancient civilization was using tablets to calculate geometric problems long before the Greeks?
Researchers at the University of New South Wales in Sydney, Australia say they have discovered just that by studying the purpose of a famous 3,700-year old Babylonian clay tablet called Plimpton 322, which they believe is actually the world鈥檚 oldest and most accurate trigonometric table.
In a new study published in Historia Mathematica, UNSW Professor Daniel Mansfield and Associate Professor Norman Wildberger argue that the small Babylonian tablet reveals an 鈥渁ncient mathematical sophistication鈥� that predates Hipparchus by more than 1,000 years.
鈥淚t opens up new possibilities not just for modern mathematics research, but also for mathematics education,鈥� Wildberger explained in a release. 鈥淲ith Plimpton 322 we see a simpler, more accurate trigonometry that has clear advantages over our own."
Plimpton 322 was discovered in the early 1900s in southern Iraq by Edgar Banks, an archaeologist who the fictional character Indiana Jones was based on, the scientists said. It鈥檚 believed the tablet may have come from the ancient Sumerian city of Larsa. It鈥檚 been dated to between 1822 and 1762 BC.
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 mathematicians demonstrate in their research how the Babylonians used a base of 60 in their numerical system instead of the more-modern base of 10 to generate numbers on the tablet.
It鈥檚 also thought to contain Pythagorean triples, or integer solutions to the Pythagorean Theorem, which was named after the Greek philosopher and mathematician Pythagoras who lived a thousand years after Plimpton 322鈥檚 dated creation.
The Sydney researchers describe the Babylonian system as a 鈥渘ovel kind of trigonometry鈥� that is based on ratios instead of angles and circles.
The findings shed new light on why the ancient scribes used Plimpton 322 in the first place. Researchers have long believed the clay tablet was intended as a teacher鈥檚 aide for checking students鈥� solutions to quadratic mathematical problems. But now, UNSW scientists believe the tablet was used for more practical purposes, such as calculating how to construct palaces, canals and temples.
鈥淭he 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,鈥� the researchers said. 鈥淧limpton 322 was a powerful tool that could have been used for surveying fields or making architectural calculations to build palaces, temples or step pyramids.鈥�
The Plimpton 322 tablet is currently housed in in New York.
