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Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)

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Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)

#111

Post by seanhunter »

Beijinger wrote: post #77

My math is a bit rusty, for a moment I was wondering about the proof of his theorem but then I realized that I messed up his theorem with the angles in a triangle that sum to 180°, which does not always hold up.

If the angles in a triangle don't add up to 180o then I think that means the triangle is not on a flat plane. An example would be if you took a point on the equator of the earth, moved East or West 1/4 of the earth's circumference and took another point and then projected those two points North until they met at the pole, you would have a triangle with 3 interior right angles.

Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)

#112

Post by loondri »

seanhunter wrote: post #108
loondri wrote: post #86

It's interesting that Pythagoras gets credit for a theorem he may not have discovered, especially when there's proof that Babylonians knew it 1000 years earlier. This challenges the idea that ancient Greek mathematicians were always ahead of others.

It's in the tradition of maths that things are named after the second person to prove them/make them well known. There are numerous examples, but one of my favourites is Venn diagrams, which were called (by Venn) "Eulerean Circles" because he took them from Euler. Everyone else is like "Nope - Venn Diagrams." It's probably just as well because otherwise just about everything would be named after Gauss which would mak…

Interesting, thanks for sharing this

Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)

#113

Post by massung »

dr_dshiv wrote: post #10

Pythagoras was specifically known for accumulating the wisdom of diverse cultures—supposedly he met Thales, was initiated as Egyptian priest in Hermopolis, spent time in Babylon after being captured, and was initiated into every mystery cult he could. And as a boy on his home island of Samos, he would have been exposed to the building of the largest stone temple in Ancient Greece (to Hera) and the incredible engineer…

Now I’m very much interested in reading more about his life! Gotta say tho, sounds a bit like an ancient Marco Polo where maybe the myth is larger than the man at this point.

Still going to read more. Thanks for the citations.

Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)

#114

Post by mcv »

travisjungroth wrote: post #46
mauvia wrote: post #22

Earlier quoted context omitted.

I know the top one is generally considered to be Euler's Equation. e^(i * pi) + 1 = 0 It's considered incredibly elegant because it manages to combine multiple fundamental mathematical concepts into a single equation. 1 is the multiplicative identity, 0 is the additive identity, pi is the circle constant, e is euler's number, i is the square root of -1, the basic building block of complex numbers.

IMO, it’s better with tau. e^(i * tau) = 1 You lose the 0, but isn’t it a bit odd the 0 is there in the first place? Normally we’d reduce it to: e^(i * pi) = -1 Which obviously isn’t as nice in this case. And hey, if we’re allowed to break the conventions, you can have the 0 back easily. e^(i * tau) = 1 + 0

Is there an easy explanation of why these are true? I already struggle grasping e^i, and I completely don't understand what e to an irrational power even means, let alone why it would be -1. Why the circle circumference ratio has anything to do with this is completely beyond me.

Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)

#115

Post by freework »

orf wrote: post #78
freework wrote: post #57

Earlier quoted context omitted.

How is this different from seeing a fuzzy video of some lights in the sky and then coming to the conclusion that it is definitely a UFO? If you're so convinced that this carving definitely proves that the carver was intending to express the Pythagorean formula, then what is the evidence? Some people's definition of "evidence" is different from my own. If somebody really wants to believe something, then just about any…

… because those “squiggles” are just “words” in a “language” you can’t “read”? And if you could read it, you would find it contains a lot of relevant things, concluding with: > … 1.414213, which is nothing other than the decimal value of the square root of 2, accurate to the nearest one hundred thousandth. You might then think to yourself: > The conclusion is inescapable. The Babylonians knew the relation between the…

Here is a drawling of what they think this tablet says:

https://commons.wikimedia.org/wiki/File:YBC_7289_sketch.svg

It's just a bunch of numbers scribbled onto a tablet. For all we know it could just be some guy writing down the number of sheep he is willing to sell to his neighbor or something. To say this tablet proves the Mesopotamian knew about Pythagorean's theorem is quite a stretch.

To the people who want to believe, there is nothing that can be said. Believe what you want.

Also, this tablet has no provenance. According to the wikipedia page on this tablet, it says "It is unknown where in Mesopotamia YBC 7289 comes from" Basically it just magically appeared one day. For all we know it could be faked. In any other field, this artifact would be ruled inauthentic. But in this field, for some reason it just doesn't matter.

Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)

#116

Post by [deleted] »

freework wrote: post #38

I've seen this tablet before, and an not convinced that it is actually the Pythagorean theorem. Its just a tablet with some tick marks inscribed onto it, along with a circular looking thing. It's very much a stretch to say the person who etched those markings intended to express the Pythagorean theorem. There was a point in time when I was very interested in ancient civilizations from Mesopotamia, but in more recent…

[deleted]

Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)

#117

Post by RetroTechie »

smokel wrote: post #47

I sometimes wonder how people will remember the invention of computers, smartphones, and the internet in a few centuries. People will most probably learn that either Bill Gates or Elon Musk invented it all in one evening when an apple fell from a tree.

History is written by some combo of historians & surviving records.

With "records" being any physical objects that outlast oral history: writings, clay tablets, the pyramids of Egypt, etc.

(and note the "surviving" bit!)

This says nothing of what really happened in the past. Only what exists in the present to support particular reconstructions of past events.

Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)

#118

Post by dr_dshiv »

massung wrote: post #113
dr_dshiv wrote: post #10

Pythagoras was specifically known for accumulating the wisdom of diverse cultures—supposedly he met Thales, was initiated as Egyptian priest in Hermopolis, spent time in Babylon after being captured, and was initiated into every mystery cult he could. And as a boy on his home island of Samos, he would have been exposed to the building of the largest stone temple in Ancient Greece (to Hera) and the incredible engineer…

Now I’m very much interested in reading more about his life! Gotta say tho, sounds a bit like an ancient Marco Polo where maybe the myth is larger than the man at this point. Still going to read more. Thanks for the citations.

Try to get a copy of the Pythagorean Sourcebook! It’s great reading original sources. So satisfying and often more interesting than modern scholarship about them.

Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)

#119

Post by vanderZwan »

Xophmeister wrote: post #88
revskill wrote: post #85

I have a curiousity. Is there a theorem or conjecture like this ? "For any irrational number, like square root of 2, we can always find the approximation of at most 3 rational numbers with just +,-,* and /" ?

If you're allowing division, you can get arbitrarily close with just two (potentially very large) integers.

I guess the more interesting conjecture would be stating something about the size of the integers compared to the irrational number

Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)

#120

Post by andrewflnr »

usrusr wrote: post #68
saithound wrote: post #5

Every group who ever managed to build a building with a rectangular foundation figured out the relation between the side lengths and the diagonal. The Egyptians used Pythagorean triples to measure right angles way before the birth of Pythagoras. But that's not a theorem, just an observation. It becomes a theorem when you prove (i.e. explain why) this relationship always holds, based on more evident things. The Babylo…

Why would you need numbers for right angles? You need a straight line and a string. But I agree with the second paragraph: there's a huge difference between a procedure that is handed down as part of "this is how we estimate a building project" and a theorem that is declared universal truth and base for all kinds of other theorems. Even if they are exactly the same thing.

I've personally worked on a project where we used a 3-4-5 right triangle to lay it out on the ground. Straight lines alone do not get you right angles.
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