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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)

#101

Post by detourdog »

dr_dshiv wrote: post #66
somenameforme wrote: post #39

Earlier quoted context omitted.

Oh how can you skip the most fun tale of them all. [1] Its authenticity is dubious, but there's probably at least parts of truth in it. In a nutshell, Pythagoras started a cult based around numbers, and the pseudo-divine purity of rational numbers - of which everything can be represented. Hippasus, a member of said cult, however managed to compellingly demonstrate that the square root of 2 could not be a rational num…

I don’t know of any ancient sources claiming that Pythagoras killed Hippasus. Seems unlikely to me! In any case, Hippasus was a fascinating figure: “Aristoxenus (Fr. 90 Wehrli = DK I 109. 31 ff.) reports that Hippasus prepared four bronze disks of equal diameters, whose thicknesses were in the given ratios, and it is true that, if free hanging disks of equal diameter are struck, the sound produced by, e.g., a disk ha…

one of my goals is a collection of educational activities based on the ground breaking earlier discoveries. Such as this.

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

#102

Post by travisjungroth »

mkl wrote: post #89
travisjungroth wrote: post #46

Earlier quoted context omitted.

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

The 0 and the + are important: e^(i*pi) + 1 = 0 contains the 5 most important constants and the three most important operations. Getting them back with "+ 0" is quite inelegant.

I don’t know. Shoving the 1 over to the left because you don’t like what it actually equals, -1, seems like an ugly hack.

Arguments better than I can make: https://tauday.com/tau-manifesto#sec-euler_s_identity

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

#103

Post by [deleted] »

somenameforme wrote: post #39
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…

Oh how can you skip the most fun tale of them all. [1] Its authenticity is dubious, but there's probably at least parts of truth in it. In a nutshell, Pythagoras started a cult based around numbers, and the pseudo-divine purity of rational numbers - of which everything can be represented. Hippasus, a member of said cult, however managed to compellingly demonstrate that the square root of 2 could not be a rational num…

[deleted]

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

#104

Post by berkes »

danjc wrote: post #80
WalterBright wrote: post #6

Earlier quoted context omitted.

> Every group who ever managed to build a building with a rectangular foundation figured out the relation between the side lengths and the diagonal. I don't see why that was necessary. You can get pretty far with eyeballing it and custom cutting to fit.

I built a tree house for my kids. I didn't exactly eyeball it but my amateur technique and planning left me having to do a lot of compensation for things being out of square. Everything becomes a custom cut, often in multiple dimensions and all earlier errors cascade all the way to the end.

> Everything becomes a custom cut, often in multiple dimensions and all earlier errors cascade all the way to the end.

Unrelated, but that sounds exactly like many software projects I've been unfortunately part of.

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

#105

Post by the_origami_fox »

For anyone wondering how they got the approximation sqrt(2)=1+24/60+51/60^2+10/60^3.

It's based on the simple idea that:

     Z = (a + b)^2 = (a^2 + (2a+b)*b)
  => (2a+b)* b
Given an initial estimate "a", we need to find the largest "b" such that the term on the left is less than the term on the right. Therefore our estimate will always be slightly less than the actual answer and we can repeat the process to get slightly closer.

For the first iteration, Z=2 and a=1. We choose b=x/60:

  (2+x/60)*x/60  3600
So our first term is 24/60.

Repeat with a=1+24/60 and b=x/60^2:

  (2(1+24/60)+x/60^2)*x/60^2 518_400
Repeat multiple times.

Writing this in code I can easily get: 1;24,51,10,7,46,6,4,44,50,28 = 1.4142135623730951

This whole process can be codified into the long division algorithm for square roots which works quite neatly with base 10.

Edit: formatting

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

#107

Post by detourdog »

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.

How useful are universal truths compared to getting shit done?

I only see theorems as useful for complex societies. The son of a gem dealer would have the time to work out universal truths.

The reputation of everyone doing it without numbers would reveal the pattern of the universal truth.

Finally this looks like it was all done using cuneiform.

Which brings up questions of notation and the language to describe a square root.

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

#108

Post by seanhunter »

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 make learning maths even more difficult than it already is.

The Pythagoreans did make a number of important discoveries to do with number theory, the ratios between string lengths for various musical notes (eg twice as long is an octave lower etc), cosmology and some other results in geometry to do with the properties of various 3-d shapes and stuff.

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

#109

Post by detourdog »

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…

I don’t mind the poor scholarship it offers opportunities to have better ideas. What I love about the ancients is that they are just like us with fewer objects.

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

#110

Post by detourdog »

mandmandam wrote: post #51
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…

I would argue with you, but you've just produced a bunch of squiggles. > It's very much a stretch to say the person who etched those markings intended to express the Pythagorean theorem. No it isn't. There are legit reasons to question a lot of the research on ancient civs, but that isn't one of them.

I agree Cuneiform tablets is a multistep process of recording an idea.
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