Posted on 08/07/2021 7:05:44 PM PDT by nickcarraway
An ancient clay tablet shows that the Babylonians used Pythagorean triples to measure accurate right angles for surveying land.
Students may not believe that Pythagoras’ Theorem has real-world uses, but a 3,700-year-old tablet proves that their maths teachers are right. The artifact, named Si.427, shows how ancient land surveyors used geometry to draw boundaries accurately.
Discovered in central Iraq in 1894, Si.427 sat in a museum in Istanbul for over a century. Now, mathematician Dr Daniel Mansfield from the University of New South Wales, Australia, has studied the clay tablet and uncovered its meaning.
“Si.427 dates from the Old Babylonian (OB) period – 1900 to 1600 BCE,” said Mansfield. “It’s the only known example of a cadastral document from the OB period, which is a plan used by surveyors define land boundaries. In this case, it tells us legal and geometric details about a field that’s split after some of it was sold off.”
As many will remember from their school days, Pythagoras’ Theorem states that the sides of a right-angled triangle obey the formula a2 + b2 = c2, where a and b are the lengths of the short sides, and c is the length of the longest side. A Pythagorean triple is a set of numbers – usually whole numbers – that fit this relation, such as 3, 4 and 5, or 5, 12 and 13. Any triangle with sides of these lengths must be a right-angled triangle.
This fact is useful for marking out accurate rectangles: constructing a triangle whose sides are a Pythagorean triple gives you a right angle every time. This makes Si.427 the earliest-known example of applied geometry.
Read more about ancient maths:
40,000-year-old yarn suggests Neanderthals had basic maths skills Archimedes: inventor of war machines and calculus (almost) “Nobody expected that the Babylonians were using Pythagorean triples in this way,” Mansfield said. “It is more akin to pure mathematics, inspired by the practical problems of the time.
“The discovery and analysis of the tablet have important implications for the history of mathematics,” he said. “For instance, this is over a thousand years before Pythagoras was born.
“This is from a period where land is starting to become private – people started thinking about land in terms of ‘my land and your land’, wanting to establish a proper boundary to have positive neighbourly relationships. And this is what this tablet immediately says. It’s a field being split, and new boundaries are made.”
However, this mathematics wasn’t always simple for the Babylonians. Their number system was different from the one we use now. Ours is in a system called base 10: numbers are written by breaking them down into hundreds, tens, units, and so on. The Babylonian number system, however, used the much more complex base 60, similar to how we keep time: 60 seconds make up one minute, and 60 minutes make up one hour.
“This raises a very particular issue – their unique base 60 number system means that only some Pythagorean shapes can be used,” said Mansfield.
In 2017, Mansfield studied another tablet from later in the same time period. This one, called Plimpton 322, contained what he calls ‘proto-trigonometry’: a table studying different types of triangle.
“It seems that the author of Plimpton 322 went through all these Pythagorean shapes to find these useful ones,” he said. “This deep and highly numerical understanding of the practical use of rectangles earns the name ‘proto-trigonometry’ but it is completely different to our modern trigonometry involving sin, cos, and tan.”
The issue of geometry and land ownership came up over and over for the ancient Babylonians, highlighting just how important this mathematics was.
“Another tablet refers to a dispute between Sin-bel-apli – a prominent individual mentioned on many tablets including Si.427 – and a wealthy female landowner,” Mansfield said.
“The dispute is over valuable date palms on the border between their two properties. The local administrator agrees to send out a surveyor to resolve the dispute. It is easy to see how accuracy was important in resolving disputes between such powerful individuals.”
As Spock would say...
I remember when BC was standard, not this BCE.
Ping-a-ling
This very poorly written article does not make the case at all for the headline’s assertion.
“when you first realize how elegant it is broken in to 3 4 5 it makes sense”
Exactly what I was thinking. Some land owner noticed that 3 4 5 worked. Them some mathematician figured out why, and applied it to other problems. Today we know a lot more, but it doesn’t mean we are smarter. It means we are building on the knowledge of the smartest people, both past and present.
Back in college I took a summer surveying course (40 years ago now). Our first project was to survey out the pretend footing of a small “L” shaped home using the transit and steel chains (probably made in the early 1950’s).
After turning the angles and measuring I figured we should check our work and I measured the various diagonals and calculating and such. In the process of doing so the professor came over.
“What are you doing!? You’re supposed to use your transit!”
“Oh - we did. Now I’m just checking the work.”
“Who told you to do this!!??”
“Um - nobody.”
“Well where the hell did you come up with this idea!!??”
“Oh - I used to help my dad build decks and patios and such - and this is how we would check our work.”
“What’s your name? What the hell group number is this!!??”
After giving him the information I asked why was that wrong and why would we be in trouble?
“Nope nothing wrong. But that is how we grade your work - so you guys get an A and saved me the trouble. And I’ve got my eye on you!”
They probably developed it when they lived in Atlantis.
Probably Iraqis & maybe some that call themselves Chaldeans.
I doubt that ANYONE involved in this article even knows who Euclid was.
Yet after the Fall and all it's physical transformations, Adam's children were said to be in his image.
From Cain came the builders and presumably the related mathematics.
Did Cain and his descendants acquire building technology on their own? Perhaps, but extra-biblical sources suggest certain ancient technologies were taught to humans.
This is just like telescopes, microscopes, and eyeglasses all of which were known to the ancient world, lost, then rediscovered hundreds or thousands of years later.
Such is real science. In REAL science, new ideas start as an hypothesis. Hypotheses are subject to the skepticisms of other REAL scientists who test their conditions. Ones that survive this testing can become theories. Such was the idea of Pythagoras. Further intense scrutiny and testing can allow some theories to become Laws. A single repeatable test can prove a thousand successes wrong. Few theories survive this scrutiny. Remember that Newton's Law of Gravity survived several centuries before it was proven inaccurate.
Yet now a few arrogant bureaucrats have determined that Catastrophic Global Warming is true science, and that Masks and Vaccines are true science. Their arrogance is eclipsed only by their ignorance.
Maybe it should be Pythagoras’s Law of right triangles.
And proves Biden really got 81 million votes.
Much of the 2 millenium babylonian science and literature is inherited from the Sumerians. They ruled in southern Iraq for nearly 2 millenium from roughly 4kbc to roughly 2kbc. Abraham the father of three religions...left Ur —one of the main cities of Sumer —at the time of the their final collapse in roughly 2k bc. the subsequent civilizations in the region merely copied the work of the sumerians in the same way that the romans copied the work of the greeks. Stories in Genesis have their echos in stories told by the sumerians—as does do the calendars of the ancient hebrews.
To this day Moslems tend to believe that adam and eve came from space. Why? The story of adam and eve has its echoes in ancient sumerian myths. The tales told by the sumerians seem to suggest that people came from space. It really reads like science fiction. This space origin of higher beings is given as an explanation for the invention of all the things that made the sumerian civilzation work for so long. However, it also suggests that there was a creative period early on that produced all the maths and sciences that enabled all the inventions of the period. But that period ended and a 1000 years later people were doing things by rote. That is, they did things because their fathers, grandfathers great grandfathers and beyond had done them that way. They had no idea how or why they came by the inventions that barbaric peoples marveled. So they said the inventions came from space beings.
I’m on online facebook threads where fans of elon musk will say the same thing of musk. He came from space. no mere human could perform his miracles. I saw a utube of Musk giving an interview in one of the gulf countries 5 years ago. The interviewer asked Musk about aliens coming to earth. Musk said that in about 20 years the civilization of earth will appear to be an alien civilization.
There was a roughly 600 year period from 500 BC to 100 AD where the greco roman world experienced high creativity and then high creativity ended. High creative activity restarted again roughly around 1500 AD and continues through to this day.
But an earlier high creative period of probably the same length likely happened in Sumeria back in the 4th millenium BC. Then that period ended. That creative period sustained Sumeria for a millenium or more —or long after the Sumerians no longer understood how or why they came by the tools and inventions they came by.
An interesting thing to note about Musk is that he has a sense that the high creative period of western civilation is coming to an end. Therefor he says that people must do everything they can do to shorten the period of the coming dark age.
Or far more likely than “space aliens” is a previous Earth civilization or several previous ones, all of whom left Earth for their own reasons, returning once in a while. 4.5 billion years is a long time and much could have/did happened.
Unfortunately my parents weren't very happy with the resultant "D" on my report card......
But if you use the proper triangles you could have turn that D into an A.
Sneaking in a musical Babylon/Mesopotamia reference here...
https://www.youtube.com/watch?v=XLfbu7NzBWI
It’s the B-52s doing an awesome live performance of their song Mesopotamia. Pretty different from their usual stuff.
Consider man’s current footprint on the earth.
Its much bigger than the black mat left by comet that ended the dinasaurs.
An earlier such civilization would have also left a footprint.
No footprint has been found.
That said, current archaelogy is placing the beginning of settled life in the middle east both before and after the big comet strike that caused the younger dryas 12k years ago. Right after the earth warmed up after the younger dryas 1000 year winter, the first big megalith was built at catalhoyuk in turkey in about 9000 BC. Anther 5 millenium passes of increasingly sophisticated village life occured before the ancient sumerians built their ziggaurats.
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