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Mathematical mystery of ancient Babylonian clay tablet solved
phys.org ^ | 08-24-2017 | Provided by: University of New South Wales

Posted on 08/25/2017 9:41:11 AM PDT by Red Badger

The 3,700-year-old Babylonian tablet Plimpton 322 at the Rare Book and Manuscript Library at Columbia University in New York. Credit: UNSW/Andrew Kelly

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UNSW Sydney scientists have discovered the purpose of a famous 3700-year old Babylonian clay tablet, revealing it is the world's oldest and most accurate trigonometric table, possibly used by ancient mathematical scribes to calculate how to construct palaces and temples and build canals.

The new research shows the Babylonians beat the Greeks to the invention of trigonometry - the study of triangles - by more than 1000 years, and reveals an ancient mathematical sophistication that had been hidden until now.

Known as Plimpton 322, the small tablet was discovered in the early 1900s in what is now southern Iraq by archaeologist, academic, diplomat and antiquities dealer Edgar Banks, the person on whom the fictional character Indiana Jones was based.

It has four columns and 15 rows of numbers written on it in the cuneiform script of the time using a base 60, or sexagesimal, system.

"Plimpton 322 has puzzled mathematicians for more than 70 years, since it was realised it contains a special pattern of numbers called Pythagorean triples," says Dr Daniel Mansfield of the School of Mathematics and Statistics in the UNSW Faculty of Science.

"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.

"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.

"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.

"This means it has great relevance for our modern world. Babylonian mathematics may have been out of fashion for more than 3000 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," he says.

The new study by Dr Mansfield and UNSW Associate Professor Norman Wildberger is published in Historia Mathematica, the official journal of the International Commission on the History of Mathematics.

A trigonometric table allows you to use one known ratio of the sides of a right-angle triangle to determine the other two unknown ratios.

The Greek astronomer Hipparchus, who lived about 120 years BC, has long been regarded as the father of trigonometry, with his "table of chords" on a circle considered the oldest trigonometric table.

"Plimpton 322 predates Hipparchus by more than 1000 years," says Dr Wildberger. "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."

Dr Mansfield read about Plimpton 322 by chance when preparing material for first year mathematics students at UNSW. He and Dr Wildberger decided to study Babylonian mathematics and examine the different historical interpretations of the tablet's meaning after realizing that it had parallels with the rational trigonometry of Dr Wildberger's book Divine Proportions: Rational Trigonometry to Universal Geometry.

The 15 rows on the tablet describe a sequence of 15 right-angle triangles, which are steadily decreasing in inclination.

The left-hand edge of the tablet is broken and the UNSW researchers build on previous research to present new mathematical evidence that there were originally 6 columns and that the tablet was meant to be completed with 38 rows.

They also demonstrate how the ancient scribes, who used a base 60 numerical arithmetic similar to our time clock, rather than the base 10 number system we use, could have generated the numbers on the tablet using their mathematical techniques.

The UNSW Science mathematicians also provide evidence that discounts the widely-accepted view that the tablet was simply a teacher's aid for checking students' solutions of quadratic problems.

"Plimpton 322 was a powerful tool that could have been used for surveying fields or making architectural calculations to build palaces, temples or step pyramids," says Dr Mansfield.

The tablet, which is thought to have come from the ancient Sumerian city of Larsa, has been dated to between 1822 and 1762 BC. It is now in the Rare Book and Manuscript Library at Columbia University in New York.

A Pythagorean triple consists of three, positive whole numbers a, b and c such that a2 + b2 = c2. The integers 3, 4 and 5 are a well-known example of a Pythagorean triple, but the values on Plimpton 322 are often considerably larger with, for example, the first row referencing the triple 119, 120 and 169.

The name is derived from Pythagoras' theorem of right-angle triangles which states that the square of the hypotenuse (the diagonal side opposite the right angle) is the sum of the squares of the other two sides.


TOPICS: Arts/Photography; Education; History; Science
KEYWORDS: algebra; babylonian; base60; ggg; greek; mathematics; trigonometery
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1 posted on 08/25/2017 9:41:11 AM PDT by Red Badger
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To: Red Badger

Pretty cool how smart ancient civilizations were...


2 posted on 08/25/2017 9:47:56 AM PDT by 2banana (My common ground with terrorists - they want to die for islam and we want to kill them)
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To: 2banana

Nothing is ever new under the Sun ...


3 posted on 08/25/2017 9:49:28 AM PDT by IWontSubmit (2)
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To: Red Badger

4 posted on 08/25/2017 9:49:43 AM PDT by Fiddlstix (Warning! This Is A Subliminal Tagline! Read it at your own risk!(Presented by TagLines R US))
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To: 2banana

When your life depends on getting the math right.................you get the math right...............


5 posted on 08/25/2017 9:50:25 AM PDT by Red Badger (Road Rage lasts 5 minutes. Road Rash lasts 5 months!.....................)
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To: IWontSubmit
... we see a simpler, more accurate trigonometry that has clear advantages over our own."

An I wasted all that time in school on the old method, sine, cosine, tangent crap........................

6 posted on 08/25/2017 9:52:13 AM PDT by Red Badger (Road Rage lasts 5 minutes. Road Rash lasts 5 months!.....................)
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To: Red Badger

What? were Babylonians Black, gay, m*slim, transsexual or peanut allergic? is this great because the Greeks are White?

I don’t care, and there is no proof that the Greeks didn’t develop it first.


7 posted on 08/25/2017 9:53:56 AM PDT by I want the USA back (Lying Media: willing and eager allies of the hate-America left.)
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To: I want the USA back
I don’t care, and there is no proof that the Greeks didn’t develop it first.

"Plimpton 322 predates Hipparchus by more than 1000 years,".................

8 posted on 08/25/2017 9:55:30 AM PDT by Red Badger (Road Rage lasts 5 minutes. Road Rash lasts 5 months!.....................)
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To: I want the USA back

The Greeks developed what we now call traditional trigonometry.

The Babylonians developed a different type of trig..................


9 posted on 08/25/2017 9:57:01 AM PDT by Red Badger (Road Rage lasts 5 minutes. Road Rash lasts 5 months!.....................)
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To: Red Badger

10 posted on 08/25/2017 10:01:38 AM PDT by Puppage (You may disagree with what I have to say, but I shall defend to your death my right to say it.)
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To: Red Badger

Interesting tablet.

But I hope everyone caught the “typo” in the fourteenth row (third column).


11 posted on 08/25/2017 10:05:29 AM PDT by ClearCase_guy (Islam: You have to just love a "religion" based on rape and sex slavery.)
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To: ClearCase_guy

The scribe transposed the < with the >...................


12 posted on 08/25/2017 10:06:48 AM PDT by Red Badger (Road Rage lasts 5 minutes. Road Rash lasts 5 months!.....................)
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To: Red Badger

And why did they need such a base 60 math system in the first place? Or was it a remnant of a previous civilization as yet undiscovered?


13 posted on 08/25/2017 10:08:50 AM PDT by PIF (They came for me and mine ... now it is your turn ...)
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To: Red Badger

Who left the friggin Dorito on the tablet?


14 posted on 08/25/2017 10:09:02 AM PDT by bar sin·is·ter (Climate Scientology - another example of science fiction morphing into a religious cult)
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To: Red Badger

15 posted on 08/25/2017 10:14:00 AM PDT by Covenantor (Men are ruled...by liars who refuse them news, and by fools who cannot govern. " Chesterton)
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To: Red Badger

Babylonian Nerds!!
Nerds!!


16 posted on 08/25/2017 10:20:05 AM PDT by right way right (May we remain sober over mere men, for God really is our one and only true hope.)
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To: lonevoice

Very cool indeed.


17 posted on 08/25/2017 10:26:34 AM PDT by Pride in the USA
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To: 2banana

The Babylonians invented the iPad.


18 posted on 08/25/2017 10:26:40 AM PDT by bar sin·is·ter (Climate Scientology - another example of science fiction morphing into a religious cult)
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To: bar sinĀ·isĀ·ter

Sheldon...................


19 posted on 08/25/2017 10:28:36 AM PDT by Red Badger (Road Rage lasts 5 minutes. Road Rash lasts 5 months!.....................)
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To: Red Badger

Mesopotamian civilization was totally unknown (outside the Bible) until a couple of centuries ago. It was the first since it had the first cities. We have just begun to scratch the surface of it.

Unfortunately, there was near constant war between these cities then empires which wound up weakening it so badly that the Persians under Cyrus (with the aid of the Jews from the Babylonian Captivity) destroyed it.

Civilizations have almost always been destroyed by invaders from the North. Ours may be unique.


20 posted on 08/25/2017 10:29:13 AM PDT by arrogantsob (Check out "CHAOS AND MAYHEM" at Amazon.com)
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