Sine o' the Times: Babylonian Tablet Holds Oldest Evidence of Trigonometry

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Sine o' the Times: Babylonian Tablet Holds Oldest Evidence of Trigonometry

Postby Edge Guerrero » Thu Aug 24, 2017 10:49 pm

By Mindy Weisberger, Senior Writer | August 24, 2017

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Researchers offer a new angle on interpreting mathematical inscriptions on a very old tablet.
Credit: UNSW


Scientists recently decoded a clay tablet from ancient Babylonia that dates to around 3,700 years ago, and found that it contains the oldest trigonometric table in the world.

The tablet, discovered in the early 1900s and first interpreted in 1945, has long fascinated mathematics scholars, but they were puzzled by its description of triangles, which researchers recently linked to a type of trigonometry.

These ancient mathematical inscriptions predate the earliest known evidence of trigonometry — thought to have originated around 120 B.C. with Greek astronomer Hipparchus — by approximately 1,000 years, the researchers reported in a new study.

This finding suggests that the Babylonians, not the ancient Greeks, were the first to study trigonometry — the mathematics of triangles — perhaps using it in architectural calculations for constructing pyramids, temples and palaces, the study authors wrote.

The tablet, which measures 5 inches (12.7 centimeters) long and 3.5 inches (8.8 cm) wide, is known as Plimpton 322, named for its owner, American philanthropist George Arthur Plimpton, who purchased the artifact in 1922 from archaeologist and antiquities dealer Edgar Banks.

Banks — the real-life inspiration for the adventure-seeking archaeologist movie character Indiana Jones — discovered the clay object in Iraq. Similarities in its writing style to that on other Babylonian tablets enabled experts to date it to between 1822 B.C. and 1726 B.C., around the time that King Hammurabi ruled the Babylonian Empire.

Experts interpreted the 15 rows of characters written in four columns on the tablet as descriptions of 15 triangles forming right angles, with their angles of inclination decreasing incrementally, the study authors wrote.

About 70 years ago, researchers determined that the notations on the tablet represented a special numerical pattern known as Pythagorean triples, a grouping of three positive integers, study co-author David Mansfield, a researcher with the School of Mathematics and Statistics at the University of New South Wales in Sydney, said in a statement.

"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," Mansfield said.

A new angle

Trigonometry analyzes the relationships between the sides and angles of triangles; it is intrinsic to geometry and plays an important role in other branches of mathematics. The study authors expanded on prior research suggesting that Plimpton 322 was broken and incomplete, and they determined that there were originally six columns of figures on the tablet. Relationships between numbers in the completed table would have represented a novel type of trigonometry — one that relied on ratios instead of angles and circles, according to the study.

Thousands of years ago, mathematicians in Babylonia used a base 60 numerical system rather than the base 10 system that forms the foundation of modern arithmetic. In the study, the authors used the ancient base 60 system to demonstrate how scribes would have arrived at the numbers that were chiseled on Plimpton 322.
"The tablet not only contains the world's oldest trigonometric table; it is also the only completely accurate trigonometric table, because of the very different Babylonian approach to arithmetic and geometry," Mansfield said.

The simplicity and accuracy of this once-lost form of Babylonian trigonometry "has clear advantages" over modern trigonometry, study co-author Norman Wildberger, an associate professor in the School of Mathematics and Statistics at the University of New South Wales in Sydney, said in the statement.

Archaeologists have uncovered numerous tablets produced during the time of the Babylonian Empire, but very few of them have been examined in detail. This study's findings hint that these understudied artifacts from a long-dead empire could hold exciting discoveries, not only for understanding the history of mathematics but also for enhancing how math is studied today, Wildberger explained.

"It opens up new possibilities not just for modern mathematics research, but also for mathematics education," he said. "The mathematical world is only waking up to the fact that this ancient but very sophisticated mathematical culture has much to teach us."

The findings were published online today (Aug. 24) in the journal Historia Mathematica.

Source: https://www.livescience.com/60227-babylonian-clay-tablet-trigonometry.html
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Postby Winnson » Fri Aug 25, 2017 12:37 pm

Interesting. It's probably a recipe for chicken soup or something, but still, interesting.

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Postby Megaterio Llamas » Fri Aug 25, 2017 9:13 pm

Winnson wrote:Interesting. It's probably a recipe for chicken soup or something, but still, interesting.



The Jewish captivity yeilding the secrets rights there.

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Postby Masato » Fri Aug 25, 2017 11:40 pm

Where Luigi at?


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Postby Luigi » Tue Aug 29, 2017 12:13 am

Yup. Its not the first time something invented by the Greeks turned out to have been invented independently by Mesopotamians 1000 years earlier. They found an Egyptian document with the pythagorian theorem on it hundreds of years before Pythagoras was born. Then they found a Babylonian tablet hundreds of years before that.
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Postby Winnson » Tue Aug 29, 2017 6:04 pm

Do you think the Greeks should pay their debts?

I think the whole EU is a major, major scam run by demented sickos. The EU are warning Hungary and Poland they need to take more refugees or else! It will be interesting to see what happens with that.

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Postby Masato » Tue Aug 29, 2017 7:41 pm

lol Winnson getting a bit off topic

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Postby Masato » Tue Aug 29, 2017 7:44 pm

So where did the Mesopotamians/Babylonians get it from?

Or did the fertile soil just spawn a sudden generation of geniuses?

What are the legends of where this civilization came from?

So weird, our history just kind of starts/stops there, no?

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Postby Megaterio Llamas » Tue Aug 29, 2017 9:38 pm

Masato wrote:So where did the Mesopotamians/Babylonians get it from?

Or did the fertile soil just spawn a sudden generation of geniuses?

What are the legends of where this civilization came from?

So weird, our history just kind of starts/stops there, no?


Mostly from the Sumerians I'd say. Well, their style anyway.

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Postby Masato » Wed Aug 30, 2017 1:16 am

^ OK, forgive my lack of ancient history

So what kind of timespan are we looking at between Sumerians - Mesopotamians - Babylonians (is that the right order?) ?

My point is that the OP suggests many great leaps of wisdom and knowledge (Pythagoras, etc) accredited to one time in history actually came from earlier times. Aren't we supposed to get dumber the farther back we go?

And if the Sumerians were doing trigonometry, where did THEY get it from? Or was THAT the great spawn of sudden mutant knowledge?

Am I wrong that conventional history suggests it just started sort of out of nowhere? What do you guys think of the case for an even more ancient civilization? I suppose even then you have to ask what pre-dated it... but then you get into aliens and gods an' shit lol


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