A new research of the University of New South Wales suggests that an ancient Babylonian tablet, referred to as Plimpton 322, is the oldest evidence of trigonometry in the world. It was discovered in the early 1900’s in Iraq. However, a lot of scientists are skeptical about the new hypothesis.

The tablet has generated a lot of debate among historians and scientists. Its cuneiform inscriptions contain a series of numbers that echo the Pythagorean Theorem, according to which the square of the hypotenuse equals the sum of the square of the other two sides. This might suggest that Babylonians actually knew some stuff about trigonometry and advanced mathematics by using the ratios of the sides of a triangle instead of the angles, sines, and cosines.

Image credit: Scientific Gems
Image credit: Scientific Gems

“It is a fascinating mathematical work that demonstrates undoubted genius,” said University of New South Wales researcher Daniel Mansfield in a press release.

The long debated truth behind the Plimpton 322

The mysterious ancient tablet was discovered at the beginning of the 20th century by the famous American archaeologist, Edgar Banks who was the inspiration for the beloved character of Indiana Jones. It was later bought by George Arthur Plimpton in 1922 (P322), and that is how it received its current name of Plimpton 322. Right now it is at the Columbia University.

However, the meaning behind the ancient Babylonian tablet is not part of the scientific consensus yet. A new research led by Mathematician Daniel Mansfield, of the University of New South Wales (UNSW) in Sydney, suggests that it could be the oldest known contribution to trigonometry, which is the study of the lengths and angles of triangles.

The clay tablet is believed to be about 3700 years old. If researchers are right, then it means that the Babylonians beat the Greeks on the use of trigonometry with a difference of 1000 years. As well, it means that the Babylonians gave an entirely different look to trigonometry. However, some scientists are completely skeptical about the new findings and say that it is just a seductive speculation. For example, Mathematical historian Christine Proust of the French National Center for Scientific Research in Paris stated that there are no Babylonian texts that would suggest that they used the clay tablet to understand triangles.

The hypothesis is “mathematically robust, but for the time being, it is highly speculative,” said Proust.

However, other scientists are not so closed-minded. For example, Mathieu Ossendrijver, a historian of ancient science at Humboldt University in Berlin, said that this new interpretation of the P322 could be right and that it would represent not only the earliest evidence of trigonometry but also an exact form of the mathematical discipline and not an approximation, as cosines and sines are. He calls this hypothesis an “open question” at the moment.

The clay tablet is believed to be about 3700 years old. Image credit: Flickr / Yahoo! News
The clay tablet is believed to be about 3700 years old. Image credit: Flickr / Yahoo! News

The shape of the tablet allows a trigonometry based on rations instead on angles

Mansfield teamed up with UNSW mathematician Norman Wildberger to study the tablet. Mansfield believes it was in fact used for trigonometric problems, but it lacks the familiar sines, cosines, and angles used by Greek astronomers and current-day students.

“It took me 2 years of looking at this [tablet] and saying ‘I’m sure it’s trig, I’m sure it’s trig, but how?” Mansfield says.

The table is arranged in a series of 15 rows intersected by four columns. Mansfield and Wildberger said that the tablet uses a base number of 60, and that would have allowed Babylonians to derive integers instead of fractions. Wildberger stated that the Babylonians must have studied trigonometry with rations instead of angles. This is because at the top of the tablet there are relatively equal ratios, and those create something like an equilateral triangle. Descending the rows of the tablets, the ratios decrease the inclination of the triangle, creating narrower ones.

The researchers say that the Babylonians might have used the trigonometry through the table to survey fields or to construct buildings. For example, with the table, they could have calculated the exact measurements they needed to build pyramid slopes.

The findings were published in the journal Historia Mathematica, the official journal for the International Commission on the History of Math.

“It is old and accurate, but the interpretation of it as a trig table is conjecture, as it is broken, and the telling part would be contained with the part broken off, and never found,” said Donald Allen, a mathematics professor at Texas A&M University, who is not part of the new research. “Bottom line is this, if interpreted as a trig table, it would be the oldest known. Some of their computations were very accurate. Babylonian arithmetic was rather clumsy, but then so were Egyptian and Greek variations.”

Currently, the father of trigonometry is believed to be The Greek astronomer Hipparchus. He lived approximately in the 120 B.C. He is known to be the one who created the table of chords drawn from the center of a circle from which he derived the widely recognized trigonometric formulas. Maybe if this new theory is proven, Hipparchus might be dethroned by the Babylonians as the father of trigonometry.

Source: National Geographic