# A 3,700-Year-Old Babylonian Clay Tablet Is Believed To Contain The World’s First Trigonometry Table

A new study reveals that a 3,700-year-old Babylonian clay tablet contains what is thought to be the oldest known trigonometry table in the world, which means that Hipparchus, the Greek astronomer, may no longer hold the title of the father of trigonometry.

Hipparchus, who lived around the time of 120 BC, is widely believed to have created trigonometry, but the Babylonian clay tablet known as Plimpton 322 has been dated to between 1822 and 1762 BC which would make it a far older system of trigonometry than the Greeks used.

The 3,700-year-old Babylonian tablet was originally found back in the early 1900s in Southern Iraq by Edgar Banks, the man reportedly used as the inspiration for the character of Indiana Jones. The tablet is believed to have originated in Larsa, an ancient Sumerian city.

Up until fairly recently, researchers were not quite sure what its purpose was. However, a team from Australia’s University of New South Wales believe that they have solved the riddle of Plimpton 322. Furthermore, the university’s team believe that the clay tablet holds lessons for us today which could help us immensely.

Daniel Mansfield, one of the researchers from the University of New South Wales, described how revolutionary this 3,700-year-old Babylonian clay tablet is, as Science Alert reports.

“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.”

Scientists have long understood that Plimpton 322 contains a list of Pythagorean triples, which are different sets of numbers with which to calculate the sides of a right-angled triangle. What has been the greatest mystery so far has been just what those triples were really there for.

In Babylonian times, the mathematics they used had a base 60, sexagesimal system instead of the decimal system or base 10 system that is in use today. When researchers analyzed Babylonian mathematical models and applied those to the 3,700-year old Babylonian tablet, they could see that when it was first created, Plimpton 322 would have had 38 rows and six columns.

It has been suggested that the tablet may have originally been used for various purposes, such as coming up with calculations for building things like temples, palaces, or other objects. Yet what has really excited researchers is the discovery that this tablet features not only the oldest trigonometry table to date, but also the most accurate one.

The reason for the astonishing accuracy of trigonometry in this 3,700-year-old Babylonian clay tablet is that you get more exact fractions with a sexagesimal system than you do with a decimal system as 60 is much easier to divide by 3. One huge advantage of this is that you don’t have to do as much rounding up. Daniel Mansfield believes that the Plimpton 322 tablet, despite its age, can teach us many new things today.

“This means it has great relevance for our modern world. Babylonian mathematics may have been out of fashion for more than 3,000 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.”

Mathematician Dr. Norman Wildberger agrees with Dr. Mansfield’s assertion that the mathematical functions of this 3,700-year-old Babylonian tablet are hugely relevant today, and notes that there are still many more Babylonian tablets left for researchers to look at, according to the Telegraph. This opens up numerous possibilities in the future, especially as only a small percentage of the other tablets in existence have been seriously studied.

“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. 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.”

The new study of this 3,700-year-old Babylonian clay tablet, which contains the oldest trigonometry table in the world, has been published in Historia Mathematica.

[Featured Image by Edward Kitch/AP Images]