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.”
Where is Hari Selden now when we need him?
Where is Hari Selden now when we need him?
As it happens. Musk is a big fan of the foundation series. So he gets his ideas about the fall and rise of civilizations from the foundation series.
That book had a big impact on me too when I was young.
An earlier such civilization would have also left a footprint.
—
In 10,000 years the current ‘footprint’ will be barely recognizable, in 20,000 years just small hills, in 100,000 years nothing not even dust, in 1,000,000 years the earth the ‘footprint’ stood on will begin to be subducted into the Earth.
Who says there is nothing left anyway? Just standard archeologists who have agendas they cannot deviate from or be ridiculed out of the profession - consensus thinking. Whose entire profession is being turned upside down with all the new tech and discoveries.
They have only assumptions and guess about who, when and why all of Earth’s Megalithic structures. They infer this, point to that, but have no actual evidence to prove they were built 5,000, 10,000, 100,000 or 1,000,000 years ago.
The Black Mat comes from the 10800 BC comet strikes, not the asteroid hit 60m years ago. The Mat was formed when the strikes began fires that grew during that 100 year period into raging firestorms across most of North America below the Ice Cap.
Occam’s razor: Its easier to postulate lost ancient Earth civilizations, then Aliens from light years away.
Dr. Ed Dutton (The Jolly Heretic) on YouTube penned a book called “At Our Wit’s End” where his thesis as that humanity is currently on a genetic downward spiral.
Some ping interesting.
Pythagoras should sue! ;^) Geometry and city-state political systems are rooted in the need to regulate competing land claims and water rights in early riverine agricultural civs, such as the Sumerians who antedate the Babylonians. :^)
Thanks for the pings!
https://freerepublic.com/focus/chat/3982026/posts?page=51#51
Most people; even Christians; miss this.
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.
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.
Without integrated circuits we are 1940s, without vacuum tubes we are 1910s, without steam we are 1800s. Once the machines of our creative period wear out we are not much better than subsistence level farmers
And that was after the Fall which resulted in a physical change to Adam & Eve causing them to be different from the way they were created. So, when Seth was born, Adam 7 Eve may have retained similarities with God’s image but they were no longer in his image.
If his point is that too many people with fatal genes are living to reproduce—and the the best genes—especially smart women — are not reproducing at all—I would be inclined to agree.
But weird stuff happens. Life finds away. There is a tremendous amount of cross breeding happening. That doesn’t weaken the species.
I can't speculate over that assumption.
I can only go by what the book actually says.
Notice the lineage of the hunmans that survived the Flood...
You married your sister? Why?
Albert Einstein's genes didn't propagate very far...
https://en.wikipedia.org/wiki/Hans_Albert_Einstein
For the shade.
Oh, you mean a bird in hand is worth two in the bush.
Well, maybe there is a point to that—especially if they’re hummingbirds gathering nectar.
Albert Einstein’s genes didn’t propagate very far...
https://en.wikipedia.org/wiki/Hans_Albert_Einstein
.........
I’m referring to a comment by Elon Musk.
https://www.goodreads.com/quotes/7170394-musk-has-talked-about-having-more-kids-and-it-s-on
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