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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)

#201

Post by tiffanyh »

Mass publication.

People typically wrongly attribute findings not to the person who first discovered it, but to the person who was able to most widely communicate/publish about it.

This is a particular difficult challenge in ancient times.

Knowledge was often shared verbally, not in written form.

Or if it was in written form, the material used has long since deteriorated.

So most of what we know about ancient thinking is based on knowledge that was so widely known and written that there's multiple copies of it; or the knowledge was communicated on a hard material like stone (egyptian hieroglyphics) ... but that doesn't mean it was the first ancients knew of it, it just means that the particular knowledge in written form has lasted the test of time the longest.

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

#202

Post by saithound »

gregjor wrote: post #82
saithound wrote: post #8

Earlier quoted context omitted.

A "you" can, and many individual "you"s presumably did that, to general satisfaction. But the implicit assumption you made is that eyeballing and cutting is easy, while triangles are hard, even though it's the other way around, especially with stone age tools. But we're talking about groups of people, "they", who all build a lot. Such groups tend to have a few people who make these observations, and then the observat…

I think you mean bronze age.

I don't think I do. I'm fairly confident that the people of the chalcolithic did enough large scale construction (and pottery and watching the night skies and so on) to have figured a whole lot of empirically accessible geometry out.

The _article_ happens to be about written sources from the Bronze Age Babylonians, which lets us glimpse at their accumulated knowledge. But there's no reason to believe this knowledge was particularly new at their time, and this was a clay tablet equivalent of an arXiv preprint.

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

#203

Post by LombardBaker »

the_origami_fox wrote: post #105

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 cl…

what evidence do you have that this is how they got it?

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

#204

Post by kridsdale3 »

maroonblazer wrote: post #145

I was surprised to learn that U.S. President Garfield devised a proof of Pythagoras' theorem. It got me wondering what other U.S. Presidents had an aptitude for math. Jefferson (3rd President) was quite fluent in geometry and surveying, designing his home in Monticello. Herbert Hoover (31st) was a mining engineer. Jimmy Carter (39th) was a nuclear engineer by training, having worked in the U.S. Navy's nuclear sub pro…

Jefferson also apparently published theorems on ideal geometric layouts of human settlement, which Salt Lake City is based on.

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

#205

Post by kridsdale3 »

gen220 wrote: post #166
maroonblazer wrote: post #145

I was surprised to learn that U.S. President Garfield devised a proof of Pythagoras' theorem. It got me wondering what other U.S. Presidents had an aptitude for math. Jefferson (3rd President) was quite fluent in geometry and surveying, designing his home in Monticello. Herbert Hoover (31st) was a mining engineer. Jimmy Carter (39th) was a nuclear engineer by training, having worked in the U.S. Navy's nuclear sub pro…

George Washington was also a surveyor before his later career(s). It was a well-trodden path to wealth and status for people of middling backgrounds and aptitudes for math and law in the pre-revolutionary U.S.

Just as Software Engineering is today.

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

#206

Post by orra »

n4r9 wrote: post #64
orra wrote: post #60

Earlier quoted context omitted.

> It becomes a theorem when you prove (i.e. explain why) this relationship always holds, based on more evident things. [...] whereas the Greeks definitely did (we don't know whether Pythagoras himself did it Wait, really? I thought the proofs back then were geometric, so only proved specific instances. And so it wasn't until algebra, maybe trig, was discovered it was properly proven?

There are fully general and valid geometric proofs, eg http://mathandmultimedia.com/wp-content/uploads/2010/02/pyth...

Despite labels $a$, $b$, $c$, I don't see how it's fully general. At best you could say it works for similar triangles, if you have that concept.

But I don't see how it proves anything if $a$ were say doubled, and $b$ kept the same.

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

#207

Post by kridsdale3 »

macintux wrote: post #200
maroonblazer wrote: post #145

I was surprised to learn that U.S. President Garfield devised a proof of Pythagoras' theorem. It got me wondering what other U.S. Presidents had an aptitude for math. Jefferson (3rd President) was quite fluent in geometry and surveying, designing his home in Monticello. Herbert Hoover (31st) was a mining engineer. Jimmy Carter (39th) was a nuclear engineer by training, having worked in the U.S. Navy's nuclear sub pro…

Obligatory link for those unfamiliar with the story: Jimmy Carter averted a full-scale nuclear meltdown in Canada at great personal risk. https://www.snopes.com/fact-check/jimmy-carter-nuclear-meltd...

And clearly that dose of radiation, in mid-1950's comic book fashion, imbued his cells with unnatural longevity!

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

#208

Post by adolph »

HideousKojima wrote: post #178
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…

TIL Terrence Howard is secretly a member of Pythagoras' math cult: https://www.independent.co.uk/news/people/terrence-howard-th... "How can it equal one? If one times one equals one that means that two is of no value because one times itself has no effect. One times one equals two because the square root of four is two, so what's the square root of two? Should be one, but we're told its two, and that cannot be."

But his success has not stopped the actor from claiming he spends up to 17 hours a day creating nameless plastic structures, which are made of cut up pieces of plastic and either stitched together with copper wire or soldered, that he believes prove his new form of mathematics.

Howard studied chemical engineering at the Pratt Institute in Brooklyn until he fell out with one of his professors over the answer to the 1x1=1 conundrum.

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

#209

Post by dang »

codethief wrote: post #97
dang wrote: post #9

Earlier quoted context omitted.

Thanks! We've changed to that from https://www.iflscience.com/pythagorean-theorem-found-on-clay... above.

Would it make sense to add (2009) to the title? I came here thinking that people discovered something new.

Ah yes. Added. Thanks!
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