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Pythagoras triangle in ancient Egypt??

 
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Were the Egyptians the first to use Pythagoras triangle?
Yes
20%
 20%  [ 1 ]
No
20%
 20%  [ 1 ]
Not sure
40%
 40%  [ 2 ]
What's Pythagoras triangle??
20%
 20%  [ 1 ]
Total Votes : 5

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Daughter_Of_SETI
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PostPosted: Sun Sep 02, 2007 7:03 pm    Post subject: Pythagoras triangle in ancient Egypt?? Reply with quote

I've read recently that Pythagoras triangle was supposedly first used in ancient Egypt back during the Old Kingdom. Is this correct, or is it just another thing that people like to attribute to the ancient Egyptians? If the Egyptians did use these triangles, could it not be coincidental? I must admit, the whole thing is pretty confusing to me seeing as I'm not all that great at maths in the first place. Crying or Very sad Were they supposed to have used these triangles when building the pyramids or something? Idea

Here's a site in favour of the Egyptians knowing of this theory : Tehuti.org

Quote:
The Egyptian concept of number symbolism was subsequently popularized in the West by and through the Greek Pythagoras (ca. 580–500 BCE). It is a known fact that Pythagoras studied for about 20 years in Egypt, soon after Egypt was open to Greek exploration and immigration (in the 7th century BCE).

Pythagoras and his immediate followers left nothing of their own writing. Yet, Western academia attributed to him and the so-called Pythagoreans, an open-ended list of major achievements. They were issued a blank check by Western academia.

Pythagoras and his followers are said to see numbers as divine concepts, ideas of the God who created a universe of infinite variety, and satisfying order, to a numerical pattern.

The same principles were stated more than 13 centuries before Pythagorus’ birth, in the heading of the Egyptian’s Rhind Papyrus, which promises,

Rules for enquiring into nature and for knowing all that exists, every mystery, every secret.


Wikipedia explains the Pythagorean theorem, and states that it was earlier used by not only the Egyptains but the Babylonians and Indians, too. Are there any ancient Egyptian artefacts that prove that the Egyptians understood the 3-4-5 triangle?

Enough questions for now. Laughing Can anyone explain all ths to me?...I'm lost! #Crazy
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isisinacrisis
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PostPosted: Sun Sep 02, 2007 7:56 pm    Post subject: Reply with quote

I really want to answer yes to this poll because I love reading about the Egyptians discovering/inventing things and ideas that we still use today and that they should be given credit to things usually attributed to other civilisations...though there are many claims I am doubtful of because people love to say 'the Egyptians invented this' because of this civilisation's mystique and popularity, but without basis in truth.
Having said that, the AEs were very good at geometry, I think I remember seeing in a few sites and books that Pythagoras visited Egypt (correct me if I'm wrong) and I remember reading in one of my books that the Egyptians constructed the 3-4-5 triangle with a knotted rope which they folded into a triangle with three knots on one side, four on another, and five on the hypotenuse.

However, I very recently saw a blog about maths for kids that says that the idea that the Egyptians knew of the 3-4-5 triangle is a myth! According to this blog, it's a story written in one of the Greek accounts of ancient Egypt-which means that it could just be hearsay. And apparently, there has been no concrete physical evidence from Egypt showing the 3-4-5 rope triangle at work.
I'm a bit surprised by this blog entry because aren't right angled triangles featured on several papyri, and what about the building of monuments like pyramids and so on? I'm not sure how much stock to put into Greek accounts of AE-some were more truthful than others but maybe because it was recorded by someone visiting Egypt in antiquity, it could be true?

Having said that, I'm a bit sceptical of that Tehuti site. I glanced at some of his books once in a bookshop, and from what I remember, the books this guy publishes seem to be borderline fringey, but then again, it's ages since I've read them so I may be confused with someone else...
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Daughter_Of_SETI
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PostPosted: Sun Sep 02, 2007 10:49 pm    Post subject: Reply with quote

isisinacrisis wrote:
Having said that, the AEs were very good at geometry, I think I remember seeing in a few sites and books that Pythagoras visited Egypt (correct me if I'm wrong) and I remember reading in one of my books that the Egyptians constructed the 3-4-5 triangle with a knotted rope which they folded into a triangle with three knots on one side, four on another, and five on the hypotenuse.

Yeah, I read that rope was supposed to have been used by the ancient Egyptians to create the the 3-4-5 triangle, too, but I've no clue as to how exactly that would work?? How would folded rope and knots make a triangle? Idea (Sorry I'm so mathematically-challenged!) Eh? Is the aim to make a set-square, or does that have nothing to do with it? Confused Yeah, I'll shut up with my idiotic questions now. Anyway, I've never heard of these ropes being discovered either, so maybe the theory's not very solid.

isisinacrisis wrote:
I'm a bit surprised by this blog entry because aren't right angled triangles featured on several papyri, and what about the building of monuments like pyramids and so on?

Are there right-angled triangles pictured in papyri? That's interesting! I don't think I've ever noticed them before. Would these knotted ropes be helpful in constructing something like the pyramids, though?

isisinacrisis wrote:
Having said that, I'm a bit sceptical of that Tehuti site. I glanced at some of his books once in a bookshop, and from what I remember, the books this guy publishes seem to be borderline fringey, but then again, it's ages since I've read them so I may be confused with someone else...

No, you're correct, Isi. The guy that owns that site is called Moustafa Gadalla, and he writes lots of bizarre theories. That's one of the reasons that I was quite sceptical about the theory of the ancient Egyptians using Pythagoras triangle myself. I still don't know what to make of it all really. Gadalla appears to use the Rhind Mathematical Papyrus as his proof, but it doesn't really seem that conclusive to me.
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kmt_sesh
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PostPosted: Mon Sep 03, 2007 12:20 am    Post subject: Reply with quote

There you go again, Daughter_Of_SETI, preaching the words of your mentor, Gadalla. Mr. Mummy would be so disappointed. Laughing

I'm only kidding. You've raised a perfectly legitimate question and I'm hesitant to step in, given that I am absolutely the most mathematically inept of all God's creatures. tard

Seriously I would like anneke to comment, as the board's resident mathematician. Part of the problem for those of us who defend orthodox history in the face of fringe scholars like Gadalla, is perhaps nothing simpler than termonology.

Applying the term "Pythagoras triangle" might be misleading but it's more than possible that the Egyptians possessed an understanding of the properties of this theorem without classifying it in any particular way. As much as I abhor Gadalla and his ilk, his reference to the Rhind papyris is valid. This text lays out some of the higher math with which the Egyptians were familiar, and demonstrates their astute knowledge of geometry as it would apply to architecture--the chief reason the Egyptians mastered mathematics.

Whether the Egyptians of the Old Kingdom were the first to hit upon something resembling the Pythagorean theorem remains debatable. Probably they were, but the architects of the only older civilization, the Sumerians, were constructing impressive ziggurat-like monuments even in their late proto-historical period (as far back as the Ubaid Period, 5000-3750 BCE). The massive platforms on which these ancient temples were constructed probably required a sharp understanding of geometry, and the oldest of these temples predate the Egyptian pyramids.

It seems clear to modern scholars that the Greeks did indeed acquire certain higher principles of mathematics from the Egyptians. To claim that they absorbed all of their mathematical skills from the Egyptians is, however, overly simplestic and unreliable. I'm not sure if Gadalla is trying to claim this, mind you, but he is correct in claiming that the Egyptians came up with a lot of mathematical concepts for which they probably haven't been given proper credit.

But do beware when Gadalla writes something like:

Quote:
Yet, Western academia attributed to him [Pythagoras] and the so-called Pythagoreans, an open-ended list of major achievements. They were issued a blank check by Western academia.


He seems to imply that Western scholars have collaborated to undermine the achievements of the older north African civilization, which is misleading and dubiously Afrocentrist. The simple truth is, scholars possessed a much firmer understanding of the ancient Greek civilization long before they acquired a suitable understanding of ancient Egypt and its achievements, and so the origins of technologies and sciences of the ancient Mediterranean were sometimes misapplied by early scholars. There is nothing so sinister about it as Gadalla would suggest.

As for the deeper discussions of the Pythagorean theorem and other things mathematical that would cause my brain to throb, I'll leave that to people who have a better grasp of the discussion. Sorry I can't be of any further help with that. Hey, I could fake my way through it, but I'd be making only more of a fool of myself than I usually do. Razz

Quote:
Are there right-angled triangles pictured in papyri? That's interesting! I don't think I've ever noticed them before.


There's no question that the Egyptians used right-angle triangles. It was the most likely method employed in establishing the angles in the foundations of pyramids, temples, and other major works of architecture. Click here for a Tour Egypt article on Egyptian mathematics. Note the photo at top of part of the famous Rhind papyrus--you can see a little diagram the scribe wrote on the mathematics of the triangle. Also, click here to see some amulets. Note the center amulet in the rightmost row--it's an amulet of a right-angle triangle, which was a very common amuletic device. There are examples of them in many museums, including the Field. The right-angle triangle would've been a common part of the kit of any Egyptian engineer and carpenter all the way back to the start of the dynastic period.
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Daughter_Of_SETI
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PostPosted: Mon Sep 03, 2007 4:42 pm    Post subject: Reply with quote

kmt_sesh wrote:
Seriously I would like anneke to comment, as the board's resident mathematician.

Me too. What have you done with Anneke, Kmt_sesh, she's disappeared? Razz Mind you, most people are maths geniuses in comparison to me. Very Happy

kmt_sesh wrote:
As much as I abhor Gadalla and his ilk, his reference to the Rhind papyris is valid. This text lays out some of the higher math with which the Egyptians were familiar, and demonstrates their astute knowledge of geometry as it would apply to architecture--the chief reason the Egyptians mastered mathematics.

Yeah, I was just checking out your TourEgypt article that you linked us to, and I see a couple of triangles depicted there. It's very interesting article, stating a couple of the mathematical problems that are written on the papyrus, but it's just a shame that a quarter of the way down the page my head started to hurt! Laughing Here's a close up of the Rhind Papyrus.

kmt_sesh wrote:
He seems to imply that Western scholars have collaborated to undermine the achievements of the older north African civilization, which is misleading and dubiously Afrocentrist. The simple truth is, scholars possessed a much firmer understanding of the ancient Greek civilization long before they acquired a suitable understanding of ancient Egypt and its achievements, and so the origins of technologies and sciences of the ancient Mediterranean were sometimes misapplied by early scholars.

I'd never thought about it quite like that, but you make a good point. Before the likes of Champollion started translating hieroglyphs, Egypt's history was a complete mystery to scholars...all they could do is stare in amazement at all the wonderful things the ancient Egyptians created without being able to understand anything in its entirity. All they had to go on was the writings of people like Herodotus to judge the Egyptians on, so I guess it's no real wonder that over recent years scholars attributed many inventions and 'firsts' to the Greeks.

I noticed on Gadalla's website that he associates the triangle with the deities Osiris, Isis, and Horus. Is that just his overactive imagination at work, or is there any eveidence of this association in ancient Egyptian artefacts or writings? Idea
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PostPosted: Mon Sep 03, 2007 9:14 pm    Post subject: Reply with quote

Quote:
What have you done with Anneke, Kmt_sesh, she's disappeared? Razz


I didn't do anything with her, honest. Anxious I just checked under my bed and in my closet and I don't seem to have stashed her there. LOL I'm sure she's very busy, between her two boys and the fall semester about to start (if it hasn't already).

Quote:
...but it's just a shame that a quarter of the way down the page my head started to hurt!


A quarter of the page down? Wow, you did a lot better than I did! Laughing

I swear, my eyes glaze over when it comes to math. I just posted the Tour Egypt article in the hopes that someone with intelligence might get something out of it. I've read translations of some of the famous Egyptian papyri but I've never gotten far with Rhind. It reminds me too much of those painful, mind-tormenting days of high school geometry. Razz

Quote:
I'd never thought about it quite like that, but you make a good point. Before the likes of Champollion started translating hieroglyphs, Egypt's history was a complete mystery to scholars...


What Champollion accomplished is the perfect example of what I was talking about. You're right, ancient Egypt was a true mystery to scholars of the time until we were able to read hieroglyphs (and of course hieratic and demotic). Before then it was supposition, guesswork, and a lot of foolish whimsy. Once ancient Egyptian was translated it opened the whole Egyptian universe to us, but long before then scholars already had a very solid understanding of the Romans and Greeks and didn't necessarily understand older cultures that contributed to them.

Quote:
I noticed on Gadalla's website that he associates the triangle with the deities Osiris, Isis, and Horus. Is that just his overactive imagination at work, or is there any eveidence of this association in ancient Egyptian artefacts or writings?


I would say that's Gadalla's fanciful mind at work, but I say that with caution because I don't have a firm grasp of Egyptian mathematics. The idea of a triad is certainly accurate, as was the case with numerous divine "families" in ancient Egypt. Maybe that's what Gadalla was trying to express. Idea
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anneke
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PostPosted: Mon Sep 03, 2007 10:21 pm    Post subject: Reply with quote

LOL I'm still here. Not as much as I would like.
kmt-sesh is right: my 2 kids and the start of the new semester are taking up almost all my time.

About the pythagorean theorem: the idea is that Pythagoras may have been the first the prove this theorem. This is why his name has been associated with it. He was not the first to know about this mathematical fact. He is suspected to have been the first to have provided a logical proof of the fact. Problem is that (to my knowledge) no writings of his exist.

All the theorem says is that in a right triangle the lengths of the sides are related via a fairly straight forward equation.

Theorems are often known quite a while before someone manages to prove them. Fermat's last theorem is a famous example. It took 300 years to prove the statement.

There is a famous "3x+1" problem now that they know is true for all numbers from 1 to something like 27 million (?). But no rigorous proof exists. We expect from empirical data that there is some pattern that is true for all possible numbers.

It seems that the mesopotamians, egyptians etc were aware of the fact that there are special right triangles. A triangle with sides 3, 4, and 5 units resp. has to be a right triangle. This is also true for a triangle with sides of length 5, 12 and 13 for instance.

From what I have seen, the egyptians knew enough mathematics to achieve quite a bit. They were able to keep accounts, they were quite accomplished at geometry (which allowed them to conduct their building projects).

They were experimental mathematicians though. They figured out how things worked by experimenting. The theoretical mathematics as we know it today is a much more recent development.

I have no idea if I have answered the question??? Cool
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PostPosted: Tue Sep 04, 2007 9:48 am    Post subject: Reply with quote

kmt_sesh wrote:
I would say that's Gadalla's fanciful mind at work, but I say that with caution because I don't have a firm grasp of Egyptian mathematics. The idea of a triad is certainly accurate, as was the case with numerous divine "families" in ancient Egypt. Maybe that's what Gadalla was trying to express.

I guess it's possible that the Egyptian triad forms the basis of Gadalla's arguement here, but it seems like he's over embellished quite a bit (which isn't new for him). I know that numbers were very significant to the ancient Egyptians, but he seems to suggest that their entire lives were ruled by numbers...to some extent they were when you look at how seriously they took their calendars, but I would think that was mostly for religious purposes and that the general population didn't care that much. Idea

anneke wrote:
About the pythagorean theorem: the idea is that Pythagoras may have been the first the prove this theorem. This is why his name has been associated with it. He was not the first to know about this mathematical fact. He is suspected to have been the first to have provided a logical proof of the fact. Problem is that (to my knowledge) no writings of his exist.

Hmm, that makes me wonder where the idea that he was the first person to prove this theory came from if there are none of his works still in existance. Did someone else - possibly from his time - write about his theory second hand and attribute the the theory to him, or something like that? If that's the case, it's not very solid evidence really, as it only tells you that by then the theory was fully established, but it may've been written about in even earlier times. Confused

anneke wrote:
All the theorem says is that in a right triangle the lengths of the sides are related via a fairly straight forward equation.

Ahh, okay, now I get it! Laughing I'm guessing that this is how some people believe that the pyramids at Giza were built - using this theory - seeing as they're supposed to be built to a very high accuracy. Very Happy

anneke wrote:
Theorems are often known quite a while before someone manages to prove them.

I suppose, in this case, that it's a fairly common arguement that people will make as to who should ultimately receive the credit: the guy who writes a theory down and explains it in its entirty V'S the people that have been using the theory for hundreds of years but never bothered to write a text about it...possibly even because the theory was like second-nature to them. Idea

anneke wrote:
They were experimental mathematicians though. They figured out how things worked by experimenting. The theoretical mathematics as we know it today is a much more recent development.

Is this where the main distinction lies with the modern person's prospective of what a true mathematcian is, do you think? Aren't some forms of mathematics 'experimental' themselves (possibly algebra??)?

Thanks for you input, Anneke. It was very helpful. Very Happy
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PostPosted: Tue Sep 04, 2007 9:01 pm    Post subject: Reply with quote

Daughter_Of_SETI wrote:

anneke wrote:
About the pythagorean theorem: the idea is that Pythagoras may have been the first the prove this theorem. This is why his name has been associated with it. He was not the first to know about this mathematical fact. He is suspected to have been the first to have provided a logical proof of the fact. Problem is that (to my knowledge) no writings of his exist.

Hmm, that makes me wonder where the idea that he was the first person to prove this theory came from if there are none of his works still in existance. ....

I think it was mentioned by some of the historians from the classical period (Plutarch?).

I'm not sure if the egyptians would have really had the full version of the theorem. Pytagoras is also credited with being the first to realize the existance of the irrational numbers. You need to know about the square root of 2 to realize that there is a "1-1-square root 2" right triangle.
I have never seen anything that indicates that the egyptians new about numbers such as the square root of 2.

But it can be a bit dangerous to try to decide what they did and did not know. We only have a limited amount of their scientific writing.


Daughter_Of_SETI wrote:

anneke wrote:
They were experimental mathematicians though. They figured out how things worked by experimenting. The theoretical mathematics as we know it today is a much more recent development.

Is this where the main distinction lies with the modern person's prospective of what a true mathematcian is, do you think? Aren't some forms of mathematics 'experimental' themselves (possibly algebra??)?

That's what I would say, yes. Euclid is credited as being the first person to set mathematics on a firm rigorous foundation.

Mathematicians still use experimentation to come up with ideas. I have spent many hours myself running calculations and seeing if there were patterns or general results that would suggest themselves. And sometimes it is very important to really understand some examples very well. But we do need to find a theoretical argument that shows our statements are true.

And there are areas that are more computational in nature. (Modern) Algebra is actually very theoretical. But there are area like "computational geometry" or computational topology". Many of these more experimental areas have overlaps with computer science.

Daughter_Of_SETI wrote:
Thanks for you input, Anneke. It was very helpful. Very Happy

You're welcome Smile I'm always a bit worried I will bore people to tears if I get too technical Cool
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PostPosted: Wed Sep 05, 2007 12:21 am    Post subject: Reply with quote

I really like the way anneke explained how these people looked at mathematics: the Egyptians were experimental mathematicians and the Greeks, theoretical mathematicians. That's the best way I've ever heard it summed up and it would behoove all of us to remember it. Smile

To the Egyptians math was a means to an end, a tool that enabled them to erect the monuments for which they are so famous. But to the Greeks, the people to whom the origins of philosophy are attributed, math seemed to be as much an art as a science, and they spent a great deal of time pondering it.

Thanks for explaining this stuff to us, anneke. We were hoping you would contribute your expertise. And I hope the semester is off to a good start for you. Wink
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PostPosted: Wed Sep 05, 2007 9:36 pm    Post subject: Reply with quote

anneke wrote:
You're welcome I'm always a bit worried I will bore people to tears if I get too technical

No, it wasn't boring in the least. You made me understand the whole thing a lot better!
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PostPosted: Sat Sep 08, 2007 4:56 am    Post subject: Reply with quote

You know, it just occurred to me that I don't think I even voted in the poll. Just for the record I'm going with "Not Sure," as I'm still wondering about those massive Mesopotamian temples in the late proto-historical period. I see by the results that others weren't sure, either.

It would be either the Mesopotamians, Egyptians, or Atlanteans. Take your pick. Very Happy
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PostPosted: Sat Sep 08, 2007 11:49 am    Post subject: Reply with quote

kmt_sesh wrote:
You know, it just occurred to me that I don't think I even voted in the poll. Just for the record I'm going with "Not Sure," as I'm still wondering about those massive Mesopotamian temples in the late proto-historical period.

Yeah, it's possible that the Mesopotamians were aware of the theory before the Egyptians. For my answer I put "What's Pythagoras Theory" because I didn't understand it at all, but from reading Anneke's explanations I understand it a little better now, so I'd probably join you with "Not Sure." Mark Lehner's The Complete Pyramids had a little bit about the theory detailed towards the back too that I've only just finished reading, which was very well explained. Wink
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PostPosted: Sat Sep 08, 2007 8:43 pm    Post subject: Reply with quote

Laughing Come to think of it, "What's Pythagoras triangle??" would've probably been the most honest answer for me, too.
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PostPosted: Sun Jun 16, 2013 11:17 pm    Post subject: Reply with quote

I thought that a problem in the Berlin Papyrus 6619 might involve a practical application of the Pythagorean theorem, and this has since been tentatively confirmed in a mainstream Egyptological journal:

"The problem is an application of the Pythagorean theorem in the calculation of two sides of a rectangle, the rule being emphasized by the choice of the square of the diagonal (= 100) as datum of the problem."

Luca Miatello, "A Debated but Little Examined Mathematical Text: Papyrus Berlin 6619," ZS 139 (2012), p. 166.

According to Miatello's interpretation, the problem deals with finding the length of the sides of a rectangle, one side 3/4 as long as the other, the combined squares on the long side and on the short side totalling 100. The rectangle is found to have a short side of 6, a long side of 8, and a diagonal of 10, the triangle formed by slicing the rectangle diagonally being a 3-4-5 right triangle.
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