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.”
Almost looks like a Babylon Bee headline.
Just because something bares a name doesn’t mean that person”invented” it. The math was always there and when you first realize how elegant it is broken in to 3 4 5 it makes sense that it has been used in architecture since we first started stacking rocks. You can make an amazing amount of structure with some string, a rock, and a couple straight sticks.
Yep, lol!
The ancient realtors wanted to get their commission and needed accurate land surveys for the parcel being sold off. Follow the money!
It’s reverse cultural appropriation!
Oh, and “bears” a name. :-)
We don’t give the ancients enough credit, I think.
In that old series, “In Search Of”, with Leonard Nimoy, everything was either a sacrificial altar or a star calendar.
The ancients were as creative as we flatter ourselves being. I think we may fail to understand some of the problems they faced.
We must reject mathematics that gives correct answers since it was invented by white people. LOL
Curious, what people that are alive today descended from the Babylonians?
Biko math
It just goes to show that if a woman feels like she’s being cheated, she will go to any length to prove it.
History of Mathematics was one of my favorite courses in undergrad. Highly recommend reading up on it you haven’t already. Of course, I assume it’s now a “woke” subject like everything else, so one probably has to go with older texts to get the truth.
ADAM had the mind of CHRIST.
It makes sense that the generations that followed ADAM were of high intellect, but their minds degenerated over time because of the fall.
Maybe some Iraqis?
“Curious, what people that are alive today descended from the Babylonians?”
“Adultlonians.”
There is nothing new under the sun.
But maths is racist!
lol!
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