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posted by Fnord666 on Saturday August 26 2017, @09:54AM   Printer-friendly
from the overrated-greeks dept.

A reexamination of a Babylonian tablet has found what may be the first appearance of trigonometry:

Consisting of four columns and 15 rows of numbers inscribed in cuneiform, the famous P322 tablet was discovered in the early 1900s in what is now southern Iraq by archaeologist, antiquities dealer, and diplomat Edgar Banks, the inspiration for the fictional character Indiana Jones.

Now stored at Columbia University, the tablet first garnered attention in the 1940s, when historians recognized that its cuneiform inscriptions contain a series of numbers echoing the Pythagorean theorem, which explains the relationship of the lengths of the sides of a right triangle. (The theorem: The square of the hypotenuse equals the sum of the square of the other two sides.) But why ancient scribes generated and sorted these numbers in the first place has been debated for decades.

Mathematician Daniel Mansfield of the University of New South Wales (UNSW) in Sydney was developing a course for high school math teachers in Australia when he came across an image of P322. Intrigued, he teamed up with UNSW mathematician Norman Wildberger to study it. "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 familiar sines, cosines, and angles used by Greek astronomers and modern-day high schoolers were completely missing. Instead, each entry includes information on two sides of a right triangle: the ratio of the short side to the long side and the ratio of the short side to the diagonal, or hypotenuse.

Mansfield realized that the information he needed was in missing pieces of P322 that had been reconstructed by other researchers. "Those two ratios from the reconstruction really made P322 into a clean and easy-to-use trigonometric table," he says. He and Wildberger concluded that the Babylonians expressed trigonometry in terms of exact ratios of the lengths of the sides of right triangles [open, DOI: 10.1016/j.hm.2017.08.001] [DX], rather than by angles, using their base 60 form of mathematics, they report today in Historia Mathematica. "This is a whole different way of looking at trigonometry," Mansfield says. "We prefer sines and cosines ... but we have to really get outside our own culture to see from their perspective to be able to understand it."

Also at the University of New South Wales.


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  • (Score: 0) by Anonymous Coward on Saturday August 26 2017, @12:53PM (1 child)

    by Anonymous Coward on Saturday August 26 2017, @12:53PM (#559414)

    Doesn't no one know where this tablet came from, so the dating is based on the style of cuneiform alone... meaning it could be easily a fake?

  • (Score: 0) by Anonymous Coward on Sunday August 27 2017, @05:51AM

    by Anonymous Coward on Sunday August 27 2017, @05:51AM (#559723)
    That it's a fake is definitely a possibility, but it can't be a fake more recent than the 1920s because the chain of provenance of the artefact is well established from that point on. It was apparently discovered by Edgar J. Banks from the ruins of the ancient city of Larsa, where there was already widespread looting by the natives, who were selling these artefacts to big museums. The first modern, scientific excavations of the site were only conducted in 1933, long after the tablet was found. However, most forgeries are easily discovered by comparing them to the real thing. Many will have inconsistencies when under heavy scientific scrutiny. Most especially if this was a forgery dating back to the 1920s, when they didn't know details of what later archaeologists have learned. No such inconsistencies were ever reported for Plimpton 322. Some artefacts once thought to be authentic were later exposed to be forgeries in that way. For instance, the fake Etruscan terra cotta statues that a pair of Italian brothers managed to con the Metropolitan Museum of Art into buying in the 1920s. They later noticed that the statues were glazed with manganese, a technique unknown to the Etruscans. Most forgeries will show such minute inconsistencies that will give them away as fakes, and Plimpton 322 hasn't shown any such inconsistencies.