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

836 点作者 samaysharma超过 1 年前

43 条评论

dr_dshiv超过 1 年前
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 engineering feat of the tunnel of Eupalinos.<p>Iamblichus’s “life of Pythagoras” [1] is worth a read as he had access to all the old sources now lost. The relationship between math and spirituality was very strong back then!<p>There are lots of fun stories that may be true but no one will ever know. In Diogenes Laertius’ “Lives of the Philosophers,” it is claimed that when Pythagoras made his discovery of what we call the Pythagorean theorem, he sacrificed 100 oxen (a hecatomb) [1]. As noted by Charles Dodgson (Lewis Carrol), “that would produce an inconvenient supply of meat” [3], especially for a vegetarian. Iamblichus, on the other hand, claims it was a single ox — and made of flour!<p>[1] Guthrie, K. S., &amp; Fideler, D. R. (Eds.). (1987). The Pythagorean sourcebook and library: an anthology of ancient writings which relate to Pythagoras and Pythagorean philosophy. Red Wheel&#x2F;Weiser.<p>[2] “he sacrificed a hecatomb, when he had discovered that the square of the hypotenuse of a right-angled triangle was equal to the squares of the sides containing the right angle.” DL, found in [1]<p>[3] Maor, E. (2019). The Pythagorean theorem: a 4,000-year history. Princeton University Press.
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saithound超过 1 年前
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.<p>But that&#x27;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 Babylonian tablet mentioned in the article doesn&#x27;t seem to do anything like that, whereas the Greeks definitely did (we don&#x27;t know whether Pythagoras himself did it, as no writing of his survives, but later Greeks knew how to do it, and attributed it to Pythagoras).
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the_origami_fox超过 1 年前
For anyone wondering how they got the approximation sqrt(2)=1+24&#x2F;60+51&#x2F;60^2+10&#x2F;60^3.<p>It&#x27;s based on the simple idea that:<p><pre><code> Z = (a + b)^2 = (a^2 + (2a+b)*b) =&gt; (2a+b)* b &lt; Z-a^2 </code></pre> Given an initial estimate &quot;a&quot;, we need to find the largest &quot;b&quot; 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.<p>For the first iteration, Z=2 and a=1. We choose b=x&#x2F;60:<p><pre><code> (2+x&#x2F;60)*x&#x2F;60 &lt; 2-1^2 120x + x^2 &lt; 3600 x = 24 ... 3456 &lt; 3600 x = 25 ... 3625 &gt; 3600 </code></pre> So our first term is 24&#x2F;60.<p>Repeat with a=1+24&#x2F;60 and b=x&#x2F;60^2:<p><pre><code> (2(1+24&#x2F;60)+x&#x2F;60^2)*x&#x2F;60^2&lt; 2-(1+24&#x2F;60)^2 10080x+x^2 &lt; 518_400 x = 51 ... 516_681 &lt; 518_400 x = 52 ... 526_864 &gt; 518_400 </code></pre> Repeat multiple times.<p>Writing this in code I can easily get: 1;24,51,10,7,46,6,4,44,50,28 = 1.4142135623730951<p>This whole process can be codified into the long division algorithm for square roots which works quite neatly with base 10.<p>Edit: formatting
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bandrami超过 1 年前
The formula wasn&#x27;t why people cared at the time; it had been empirically known for centuries. What caused such a stir was he was the first person to prove that for &quot;most&quot; right triangles there are no rational numbers P, Q such that PA = QC for leg A and hypotenuse C. <i>That</i> was what was earth-shaking.
nologic01超过 1 年前
Its only fitting that the now defunct &quot;Journal for Targeting, Measurement and Analysis for Marketing&quot; would have a clickbaity and misleading title on an article that seems completely off-topic and of very poor quality. A Springer sponsored precursor to the SEO driven abominations of today maybe?<p>Confusing calculation with proof is an inexcusable mistake for any serious journal.<p>There can be little doubt that proving theorems is a cognitive tool that developed on the basis of observed regularities. But both asking the question <i>why</i> and, importantly, <i>answering it using logic</i> are highly non-trivial developmemts.
lynguist超过 1 年前
The mainstream is and was _enamored_ with Ancient Greece.<p>Our Western culture made Ancient Greek into the vocabulary root of our sciences.<p>We have a lineage of philosophy from Ancient Greece to the 19th century.<p>Only in the 19th century with archeology (again a neo-word made from Ancient Greek roots – it suggests to the mainstream that the Ancient Greek had a concept of archaeology, which they obviously didn’t have) we saw the truth: History goes thousands of years deeper, the origin of everything is thousands of years older.<p>Only 30 years ago the capital city of Hattuša was discovered; and only in the 20th century we gained an understanding of the multiple levels of the historic city of Troy.<p>Only recently we understand that &quot;it didn’t start with Ancient Greece&quot;, but the mainstream still follows the tradition of medieval grammar schools and doesn’t look beyond Ancient Greece.
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Tainnor超过 1 年前
The article claims that the Babylonians &quot;discovered&quot; the Pythagorean theorem, but all it shows is that they (probably) believed it to be true.<p>Until we have better evidence, it still seems to be the case that (at least in the &quot;West&quot;, I&#x27;m unfamiliar with e.g. Chinese mathematics) the Greeks were the first to come up with the concept of a mathematical proof that is valid deductively, and not inductively.
tiffanyh超过 1 年前
Mass publication.<p>People typically wrongly attribute findings not to the person who first discovered it, but to the person who was able to most widely communicate&#x2F;publish about it.<p>This is a particular difficult challenge in ancient times.<p>Knowledge was often shared verbally, not in written form.<p>Or if it was in written form, the material used has long since deteriorated.<p>So most of what we know about ancient thinking is based on knowledge that was so widely known and written that there&#x27;s multiple copies of it; or the knowledge was communicated on a hard material like stone (egyptian hieroglyphics) ... but that doesn&#x27;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.
helsinkiandrew超过 1 年前
Discussion on HN 7 years ago about parallel proofs after discovery in a 2600 year old Chinese book:<p><a href="https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=13952265">https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=13952265</a>
personjerry超过 1 年前
I know it was known in China at least before Pythagoras <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Zhoubi_Suanjing" rel="nofollow noreferrer">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Zhoubi_Suanjing</a>
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chx超过 1 年前
As a side note Dijkstra has a wonderful generalization and it has a nice proof at <a href="https:&#x2F;&#x2F;www.cut-the-knot.org&#x2F;pythagoras&#x2F;Stevens.shtml" rel="nofollow noreferrer">https:&#x2F;&#x2F;www.cut-the-knot.org&#x2F;pythagoras&#x2F;Stevens.shtml</a> and I was wondering whether this is old as well.
loganc2342超过 1 年前
&gt; <i>The Pythagorean Theorem is arguably the most famous statement in mathematics, and the fourth most beautiful equation.</i><p>Just out of curiosity, which equations are considered the top three “most beautiful?”
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leke超过 1 年前
Kind of reminds me of that &quot;Bro, I stole your code&quot; - &quot;It&#x27;s not my code&quot; meme.
teleforce超过 1 年前
Contributions to the body of knowledge is not and never ever been monopolized by any particular nation or civilization but if you read most modern textbooks you&#x27;re forgiven to think that it was all started with Greek civilization and then nothing of significance happened until Renaissance movement in the 14th CE (conveniently skipping the contributions of the Roman (namely Rome and Byzantine) and Muslim empires (namely Rashidun, Umayyad, Abassid, Andalusian Spanish, Ottoman)). A popular Monty Python sketch of &quot;What have the Roman&#x27;s done to us&quot; perfectly summarized this ridiculous sentiment.[1]<p>The fact that many contributions from other older civilizations for examples Indus Valley (Indian) where the original cuneiform alphabet was started and Phoenician (Arabic) where most of the modern alphabets (Latin, Greek, Arabic, Sanskrit) originated. The former Indus Valley script has not even been successfully deciphered yet until today (Nobel price in waiting for the ones who will deciphered them), perhaps they are some older proofs that are just waiting to be discovered upon the understanding of the Indus Valley scripts and languages.<p>But the nonsensical narrative of whom has the monopoly of contributions to knowledge will carry on until the end of time but the reality is that we are just standing on the shoulders of giants [2].<p>[1] What have the Roman&#x27;s done to us:<p><a href="https:&#x2F;&#x2F;youtu.be&#x2F;kCXoUZSgE08" rel="nofollow noreferrer">https:&#x2F;&#x2F;youtu.be&#x2F;kCXoUZSgE08</a><p>[2]Standing on the shoulders of giants:<p><a href="https:&#x2F;&#x2F;en.m.wikipedia.org&#x2F;wiki&#x2F;Standing_on_the_shoulders_of_giants" rel="nofollow noreferrer">https:&#x2F;&#x2F;en.m.wikipedia.org&#x2F;wiki&#x2F;Standing_on_the_shoulders_of...</a>
Perenti超过 1 年前
I recall seeing that there was a 14 000 year old dear scapula found in China that had the &quot;simple proof&quot; diagram engraved on it. The article seems to say that Pythagoras&#x27; Theorem was discovered by the Mesopotamians, but neglects mentioning it may be _much_ older.<p>Someone above commented that just by building ancient peoples would have discovered this relationship.
Vt71fcAqt7超过 1 年前
Has anyone found the source for that tablet? All I have found is this:<p>&gt;Note that quite a few descriptions on Babylonian tablets seem to cite a translation of a Pythagorean algorithm from a ca. 1900BC tablet by a Dennis Ramsey – I have not been able to find the original source of this anywhere.[0]<p>The linked arctile cites wikipedia and bible-history.com. This book[1] misquotes the supposed tablet as being ycb 7289, probably because these tablets are referenced next to each other on wikipedia.<p>This[2] website says it&#x27;s in the British museum.<p>[0]<a href="https:&#x2F;&#x2F;craftofcoding.wordpress.com&#x2F;author&#x2F;spqr&#x2F;" rel="nofollow noreferrer">https:&#x2F;&#x2F;craftofcoding.wordpress.com&#x2F;author&#x2F;spqr&#x2F;</a><p>[1]<a href="https:&#x2F;&#x2F;books.google.com&#x2F;books?id=XDBCEAAAQBAJ&amp;pg=PT257&amp;lpg=PT257&amp;dq=%224+is+the+length+and+5+is+the+diagonal.+What+is+the+breadth?+Its+size+is+not+known.+4+times+4+is+16.+And+5+times+5+is+25.+You+take+16+from+25+and+there+remains+9.+What+times+what+shall+I+take+in+order+to+get+9?+3+times+3+is+9.+3+is+the+breadth%22&amp;source=bl&amp;ots=rpq5LBD67m&amp;hl=en&amp;sa=X&amp;ved=2ahUKEwj514O-hN-BAxWmvokEHZDhCV0Q6AF6BAgJEAE#v=onepage&amp;q=%224%20is%20the%20length%20and%205%20is%20the%20diagonal.%20What%20is%20the%20breadth%3F%20Its%20size%20is%20not%20known.%204%20times%204%20is%2016.%20And%205%20times%205%20is%2025.%20You%20take%2016%20from%2025%20and%20there%20remains%209.%20What%20times%20what%20shall%20I%20take%20in%20order%20to%20get%209%3F%203%20times%203%20is%209.%203%20is%20the%20breadth%22&amp;f=false" rel="nofollow noreferrer">https:&#x2F;&#x2F;books.google.com&#x2F;books?id=XDBCEAAAQBAJ&amp;pg=PT257&amp;lpg=...</a><p>[2]<a href="https:&#x2F;&#x2F;mathshistory.st-andrews.ac.uk&#x2F;HistTopics&#x2F;Babylonian_Pythagoras&#x2F;" rel="nofollow noreferrer">https:&#x2F;&#x2F;mathshistory.st-andrews.ac.uk&#x2F;HistTopics&#x2F;Babylonian_...</a>
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mjfl超过 1 年前
did they know about the Pythagorean theorem, or did they know about the square root of two? It seems that people did puzzle over this quantity for a while.
layer8超过 1 年前
&gt; Why did the scribe choose a side of 30 for his example?<p>Clearly because that makes the answer for the diagonal 42.
bagels超过 1 年前
Diogenes said that Pythagoras hated beans: “One should abstain from fava beans, since they are full of wind and take part in the soul, and if one abstains from them one’s stomach will be less noisy and one’s dreams will be less oppressive and calmer.”
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renewiltord超过 1 年前
Stigler&#x27;s law of eponymy <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Stigler%27s_law_of_eponymy" rel="nofollow noreferrer">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Stigler%27s_law_of_eponymy</a>
zestyping超过 1 年前
<a href="https:&#x2F;&#x2F;personal.math.ubc.ca&#x2F;~cass&#x2F;Euclid&#x2F;ybc&#x2F;ybc.html" rel="nofollow noreferrer">https:&#x2F;&#x2F;personal.math.ubc.ca&#x2F;~cass&#x2F;Euclid&#x2F;ybc&#x2F;ybc.html</a><p>This is the original site about the tablet and has more detail and analysis than the Springer article.<p><a href="https:&#x2F;&#x2F;personal.math.ubc.ca&#x2F;~cass&#x2F;Euclid&#x2F;ybc&#x2F;analysis.html" rel="nofollow noreferrer">https:&#x2F;&#x2F;personal.math.ubc.ca&#x2F;~cass&#x2F;Euclid&#x2F;ybc&#x2F;analysis.html</a>
revskill超过 1 年前
I have a curiousity.<p>Is there a theorem or conjecture like this ?<p>&quot;For any irrational number, like square root of 2, we can always find the approximation of at most 3 rational numbers with just +,-,* and &#x2F;&quot; ?
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mayd超过 1 年前
This discussion leaves unclear the the role of Pythagoras of Samos in the discovery of the Pythagorean Theorem. The statement of the theorem appears to have been known before the time of Pythagoras. He is credited with giving the first proof of the theorem, within the framework of Greek mathematics. On that claim his fame rests, although no record of his proof has survived.
maroonblazer超过 1 年前
I was surprised to learn that U.S. President Garfield devised a proof of Pythagoras&#x27; theorem. It got me wondering what other U.S. Presidents had an aptitude for math.<p>Jefferson (3rd President) was quite fluent in geometry and surveying, designing his home in Monticello.<p>Herbert Hoover (31st) was a mining engineer.<p>Jimmy Carter (39th) was a nuclear engineer by training, having worked in the U.S. Navy&#x27;s nuclear sub program.
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smokel超过 1 年前
I sometimes wonder how people will remember the invention of computers, smartphones, and the internet in a few centuries.<p>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.
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wly_cdgr超过 1 年前
Impossible! Pythagoras wasn&#x27;t born yet!
cobbzilla超过 1 年前
According to Shaquille [1], it’s still an unsolved problem.<p>[1] <a href="https:&#x2F;&#x2F;www.brainyquote.com&#x2F;quotes&#x2F;shaquille_oneal_381872" rel="nofollow noreferrer">https:&#x2F;&#x2F;www.brainyquote.com&#x2F;quotes&#x2F;shaquille_oneal_381872</a>
Beijinger超过 1 年前
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.
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jeisc超过 1 年前
Names are important as they indicate things; maybe Triangle Theorems would be better to cover the properties of triangles; perhaps there are other ones which we missed discovering... hubris has no limits
stainablesteel超过 1 年前
i&#x27;m not surprised<p>basic geometry was probably fundamental to the architecture necessary to make civilizations<p>i&#x27;d bet that as far back as we can find large structure there would probably have been strong understandings of geometry to make them<p>plus, humans have been around for 200-300k years, what we can find is from ~12k-25k years ago at the very fringe of our investigations. no doubt people have been mathematically capable for longer than they&#x27;ve been able to take full advantage of the concepts they understand
zeroonetwothree超过 1 年前
The original example of Stigler’s law of eponymy.
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pyninja超过 1 年前
So many red flags in the abstract alone. It&#x27;s no surprise that the article itself looks like a middle school project.
abhinai超过 1 年前
It needs to be renamed as the Tablet Theorem.
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jaystraw超过 1 年前
Anyone in the threads I collapsed should buy a speed square and read the booklet. Possibly over beer or tea.
xwowsersx超过 1 年前
&gt; who uses the theorem two decades later for something about relatively<p>I assume that should read relativity*?
bzmrgonz超过 1 年前
This probably went up in smoke along soo many other knowledge gems at the Alexandria Library!!
voisin超过 1 年前
Why was this published in the Journal of Targeting, Measurement and Analysis for Marketing?
eruci超过 1 年前
Prior art - Even Pythagoras didn&#x27;t come up with Pythagoras&#x27;s Theorem.
mindblown9超过 1 年前
How did he live for so long?!
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loondri超过 1 年前
It&#x27;s interesting that Pythagoras gets credit for a theorem he may not have discovered, especially when there&#x27;s proof that Babylonians knew it 1000 years earlier.<p>This challenges the idea that ancient Greek mathematicians were always ahead of others.
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zacharycohn超过 1 年前
So Pythagoras also invented time travel??
umeshunni超过 1 年前
Actual paper from 2009: <a href="https:&#x2F;&#x2F;link.springer.com&#x2F;article&#x2F;10.1057&#x2F;jt.2009.16" rel="nofollow noreferrer">https:&#x2F;&#x2F;link.springer.com&#x2F;article&#x2F;10.1057&#x2F;jt.2009.16</a><p>Link above is clickbait blogspam (like most things on IFLScience)
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freework超过 1 年前
I&#x27;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&#x27;s very much a stretch to say the person who etched those markings intended to express the Pythagorean theorem.<p>There was a point in time when I was very interested in ancient civilizations from Mesopotamia, but in more recent years I an way less interested in it. The scholarship in that field is just terrible. In my opinion, a lot of the stuff is on par with alien &quot;investigators&quot; and stuff like that, yet for some reason the general public sees the field as totally legit.
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