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posted by martyb on Friday August 20 2021, @11:47PM   Printer-friendly

Babylonian Tablet Trigonometry:

Contrary to what generations of pupils have learned in high school geometry, the Greek philosopher Pythagoras did not come up with this foundational theorem [(a² + b² = c²)] first. The proof lies in an ancient artifact that dates back to the Old Babylonian (OB) period: 1900 to 1600 B.C.

In 1894, Father Jean-Vincent Scheil excavated a clay tablet at an archaeological expedition at Sippar, southwest of Baghdad. "But its significance was not understood at the time," Daniel Mansfield—lead author of the new research and a mathematician at the University of New South Wales in Sydney, Australia—writes in The Conversation.

The tablet, known as Si.427, is "the only known example of a cadastral document from the OB period, which is a plan used by surveyors to define land boundaries," according to Mansfield. On the front of the artifact is an inscription showing a diagram of a field. The surveyors drew a series of perpendicular lines, using Pythagorean triples to create precise right angles so that the fields' boundaries were as square as possible.

There's evidence of triangles drawn around the periphery of the field documented on the tablet, but if that's not enough proof, consider the back of the clay tablet. On it, cuneiform text describes the opposite side, including details about the sizes of the fields.

[...] Surveyors used Pythagorean triples to measure fields and draw accurate maps, but some numbers that make up Pythagorean triples aren't regular, and don't make sense to try to scale up to fit any field. Plimpton 322 lists a bunch of Pythagorean triples and notes which of their three values is regular, helping ancient Babylonian surveyors to quickly "do the math," so to speak.

Journal Reference:
Mansfield, Daniel F.. Plimpton 322: A Study of Rectangles [open], Foundations of Science (DOI: 10.1007/s10699-021-09806-0)


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  • (Score: 2, Troll) by Runaway1956 on Friday August 20 2021, @11:59PM (8 children)

    by Runaway1956 (2926) Subscriber Badge on Friday August 20 2021, @11:59PM (#1169116) Journal

    Sadists decided to give Pythagoras credit because his name is so hard to spell, or remember. Easier to remember "Some dead Greek said a square plus b square equal c square, but my yard isn't even square!"

    --
    We've finally beat Medicare! - Houseplant in Chief
    • (Score: 0, Troll) by aristarchus on Saturday August 21 2021, @09:19AM (7 children)

      by aristarchus (2645) on Saturday August 21 2021, @09:19AM (#1169230) Journal

      Truly you are an ignorant moron, Runaway! I suppose you think Greeks can pronounce "Paul Cooper", just for example, any easier? And, if you can't do math, perhaps you should not comment?

      • (Score: 2) by kazzie on Saturday August 21 2021, @01:07PM (2 children)

        by kazzie (5309) Subscriber Badge on Saturday August 21 2021, @01:07PM (#1169277)

        I'm not here to do math, but to mention how tickled I was to see restaurants on Lesvos advertising "roast lamp" to the tourists.

        • (Score: 4, Interesting) by kazzie on Saturday August 21 2021, @01:13PM (1 child)

          by kazzie (5309) Subscriber Badge on Saturday August 21 2021, @01:13PM (#1169278)

          To explain the joke, the Greek alphabet has no letter corresponding to the sound 'b', so uses a digraph of 'mp' (or rather 'μπ') to represent that sound.

          "What about bete" , you say? That represents a 'v' sound, hence the confusion with placenames like Lesvos/Lesbos.

      • (Score: 0) by Anonymous Coward on Saturday August 21 2021, @03:43PM

        by Anonymous Coward on Saturday August 21 2021, @03:43PM (#1169298)

        Arnold Palmer is out as well?

      • (Score: 2) by Runaway1956 on Sunday August 22 2021, @12:28AM (2 children)

        by Runaway1956 (2926) Subscriber Badge on Sunday August 22 2021, @12:28AM (#1169456) Journal

        Still phishing, I see? I missed that the first time I looked at your post. Keep trying!

        --
        We've finally beat Medicare! - Houseplant in Chief
        • (Score: 0) by Anonymous Coward on Sunday August 22 2021, @06:52AM (1 child)

          by Anonymous Coward on Sunday August 22 2021, @06:52AM (#1169539)

          OK, Paul. Spearing confirmed.

  • (Score: -1, Troll) by Anonymous Coward on Saturday August 21 2021, @01:31AM (1 child)

    by Anonymous Coward on Saturday August 21 2021, @01:31AM (#1169137)

    Tablet? In the Middle East? Probably just a cheap iPad knockoff imported from China.

    • (Score: 0) by Anonymous Coward on Saturday August 21 2021, @03:54PM

      by Anonymous Coward on Saturday August 21 2021, @03:54PM (#1169300)

      yep, it took this long to discover because they were waiting for electricity to be invented to charge the tablet after first use.

  • (Score: 5, Interesting) by bzipitidoo on Saturday August 21 2021, @02:02AM (16 children)

    by bzipitidoo (4388) on Saturday August 21 2021, @02:02AM (#1169146) Journal

    In chess problem composition circles, repetition happens so often there's a term for it: anticipated. So often, some chess player composes what they thought was a new chess problem, only to be told that someone else had already done almost the same thing a century ago. Seems the problem space is just too small. Pop music also has this problem, though not as much as chess composition. There are only a relatively few, finite number of short melodies.

    The Pythagorean Theorem is obviously too basic and easy to take exceptional, once in a millennium mathematical genius to discover. Main reason we credit the Greeks with so much early math is their records are much better known than Bronze Age records. Knowledge of the ancient Greek and Latin languages was never lost, while cuneiform was. Cuneiform was relearned only in the 19th century.

    One little thing I've been wondering is why so many of these ancient languages went extinct in the 1st century, rather than much earlier, like, during the dark age between the Bronze and Iron Ages. The last known cuneiform tablet, according to a quick check of Wikipedia, was written in 75 AD. What happened to end cuneiform at that time in history? It wasn't a particularly devastating period. Yet use of cuneiform writing, Aramaic, Egyptian hieroglyphs, and other languages and writing systems all ended around that time.

    • (Score: -1, Redundant) by Anonymous Coward on Saturday August 21 2021, @02:15AM (1 child)

      by Anonymous Coward on Saturday August 21 2021, @02:15AM (#1169148)

      TL;DR.

      What a windbag.

      • (Score: 1, Informative) by Anonymous Coward on Saturday August 21 2021, @02:19AM

        by Anonymous Coward on Saturday August 21 2021, @02:19AM (#1169150)

        So says the illiterate buffoon who couldn't read parent post.

    • (Score: 2, Funny) by Anonymous Coward on Saturday August 21 2021, @02:18AM

      by Anonymous Coward on Saturday August 21 2021, @02:18AM (#1169149)

      What happened to end cuneiform at that time in history?

      The humans stopped worshiping cats, so cats withdrew their knowledge and wisdom from mankind. BTW, look at those cuneiform tablets again. The markings are obviously made by cat's claws. A stylus is just a poor imitation of a claw.

    • (Score: 2, Interesting) by Anonymous Coward on Saturday August 21 2021, @02:36AM (5 children)

      by Anonymous Coward on Saturday August 21 2021, @02:36AM (#1169153)

      Weren't the Romans busy expanding their empire in those directions around then?

      • (Score: 0) by Anonymous Coward on Saturday August 21 2021, @12:00PM (4 children)

        by Anonymous Coward on Saturday August 21 2021, @12:00PM (#1169270)

        Historical ignorance like this makes SoylentNews look stupid. Next thing, you will be claiming Greeks wore Togas. On the basis of Animal House.

        • (Score: 2, Touché) by FatPhil on Saturday August 21 2021, @06:04PM (3 children)

          by FatPhil (863) <pc-soylentNO@SPAMasdf.fi> on Saturday August 21 2021, @06:04PM (#1169344) Homepage
          So there was no conquest of Britain after all, they all stayed at home and had a nice glass of wine with their dormouse? Residents of Dacia likewise remember ten consecutive years of no invading forces. Germanicus was fake news?

          Historical ignorance like yours does indeed make SoylentNews look stupid, so please desist.
          --
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          • (Score: 3, Informative) by aristarchus on Sunday August 22 2021, @12:26AM (2 children)

            by aristarchus (2645) on Sunday August 22 2021, @12:26AM (#1169455) Journal

            Pythagoras died in 495 B.C. Romans still had a king, then. Britannia was not permanently occupied by Romans until 43 A. D. , some five hundred plus years after Pythagoras.

            Historical ignorance like yours does indeed make SoylentNews look stupid, so please desist.

            In fact, during his later years, Pythagoras lived in the town of Croton, in Magna Graeci, southern Italy, not bothered at all by the city of outcasts to the north.

            • (Score: 2) by FatPhil on Sunday August 22 2021, @07:58AM (1 child)

              by FatPhil (863) <pc-soylentNO@SPAMasdf.fi> on Sunday August 22 2021, @07:58AM (#1169544) Homepage
              The question was:
              >>>> One little thing I've been wondering is why so many of these ancient languages went extinct in the 1st century, rather than much earlier

              The answer proffered was:
              >>> Weren't the Romans busy expanding their empire in those directions around then?

              To which the idiot AC responded with idiocy remarkably aligned with the idiocy you're now spouting.
              To which I posted a correction.

              Enter stage left another idiot who thinks Pythagoras has something to do with the 1st century...
              Apologies for having to spell out the mistake you're making in such gory detail, but you are being remarkably slow.
              --
              Great minds discuss ideas; average minds discuss events; small minds discuss people; the smallest discuss themselves
              • (Score: 2, Funny) by aristarchus on Sunday August 22 2021, @08:46AM

                by aristarchus (2645) on Sunday August 22 2021, @08:46AM (#1169550) Journal

                Learn to blockquote. And if I had mod points, I would grow a vagina on your arm!

                This is why Anglish-sprache is a dead language?

    • (Score: 5, Interesting) by ikanreed on Saturday August 21 2021, @03:35AM (5 children)

      by ikanreed (3164) Subscriber Badge on Saturday August 21 2021, @03:35AM (#1169161) Journal

      The theory I've heard is that Pythagoras was a cult leader [classicalwisdom.com] and his "school" that attached his name to the theorem also attributed a ton of other by-then well-established facts to him, but the triangle one was the only one that stuck.

      • (Score: 1, Offtopic) by shortscreen on Saturday August 21 2021, @06:05AM (2 children)

        by shortscreen (2252) on Saturday August 21 2021, @06:05AM (#1169178) Journal

        Quite right. Pythagoras lead a cult of ninja assassins [wikipedia.org].

        • (Score: 2) by kazzie on Saturday August 21 2021, @01:16PM (1 child)

          by kazzie (5309) Subscriber Badge on Saturday August 21 2021, @01:16PM (#1169281)

          But why were they assasinating the ninjas?

          • (Score: 0) by Anonymous Coward on Sunday August 22 2021, @12:32AM

            by Anonymous Coward on Sunday August 22 2021, @12:32AM (#1169457)

            Pirates, of course.

      • (Score: 2) by pipedwho on Saturday August 21 2021, @01:14PM

        by pipedwho (2032) on Saturday August 21 2021, @01:14PM (#1169279)

        Interesting link. They describe a bunch of things that aren’t consistent with Pythagoras unless he was an idiot. They also tear down his spirituality like it’s some sort of physical superstition while describing it almost identically to Buddhism.

        The cult thing seems possible, but it’s like describing christians as the cult of Jesus. (Which for some/most?
          ‘churches’ is about right).

      • (Score: 1, Interesting) by Anonymous Coward on Saturday August 21 2021, @04:31PM

        by Anonymous Coward on Saturday August 21 2021, @04:31PM (#1169310)

        There is no reliable evidence [blogspot.com] that Pythagoras had anything to do with the theorem; among other things, the only ancient writers crediting him with it lived many centuries after his time. The Babylonians definitely knew the formula, though they almost certainly had no proof.

    • (Score: 0) by Anonymous Coward on Saturday August 21 2021, @08:13AM

      by Anonymous Coward on Saturday August 21 2021, @08:13AM (#1169221)

      Aliens had enough of us and left the planet.

  • (Score: 4, Interesting) by HiThere on Saturday August 21 2021, @03:03AM (3 children)

    by HiThere (866) Subscriber Badge on Saturday August 21 2021, @03:03AM (#1169159) Journal

    Pythagoras clearly didn't invent right triangle measurements. He *MAY* have been the first to show that right triangles in general have the sum of squares property. And this tablet doesn't speak to this point.

    E.g. the Egyptians at least used many specific right triangles in dividing up the land boundaries after the Nile flooded and erased the previous markers. I don't know that it's been shown that they knew that all right triangles had the a^2 + b^2 = c^2 property, but they certainly knew that about several of them, and that's all this tablet really demonstrates.

    Of course, this doesn't prove Pythagoras was first. But he *could* have been the first to solve it as a general problem...AFAIK. Special cases, even lots of them, don't prove the general problem. (Though they can be a very strong indication.)

    --
    Javascript is what you use to allow unknown third parties to run software you have no idea about on your computer.
    • (Score: 5, Troll) by aristarchus on Saturday August 21 2021, @09:25AM

      by aristarchus (2645) on Saturday August 21 2021, @09:25AM (#1169233) Journal

      I would request some more respect for my fellow Samian. Yes, what we Greeks did with math had earlier sources. We never hid that. Pythagoras was innovative in his application of Egyptian geometry, for example applying triangulation to offshore navigation and position fixing. Geo-metry into Thalassa-metry. So give credit where credit is due, without neglecting out debt to those before us.

      And you should know, the majority of my education, and teaching, was in Alexandria, which as you
      Americans may not know, it is Africa.

    • (Score: 5, Insightful) by legont on Saturday August 21 2021, @09:47AM

      by legont (4179) on Saturday August 21 2021, @09:47AM (#1169250)

      What attributed to Pythagoras is a proof. The conjecture, off course, was known and used in everyday life way before him (so the news is over-hyped).

      --
      "Wealth is the relentless enemy of understanding" - John Kenneth Galbraith.
    • (Score: 0) by Anonymous Coward on Tuesday August 24 2021, @09:43AM

      by Anonymous Coward on Tuesday August 24 2021, @09:43AM (#1170234)

      if you search for "egyptian triangle", you find stuff like https://mathvox.com/egyptian-triangle/ [mathvox.com] . I don't have a better source (other than teachers mentioning it in class, I think), but I think it's a fairly common bit of trivia that egyptians knew you can get a right angle if you build a triangle with sides 3, 4 and 5 --- and I assume you don't need that much brain to figure out some similarly simple useful number sequences.

  • (Score: -1, Spam) by Anonymous Coward on Saturday August 21 2021, @07:03AM (1 child)

    by Anonymous Coward on Saturday August 21 2021, @07:03AM (#1169204)

    I just want to grow a vagina on my arm

    • (Score: 0) by Anonymous Coward on Saturday August 21 2021, @10:52PM

      by Anonymous Coward on Saturday August 21 2021, @10:52PM (#1169416)

      Sorry, all we can do is ears right now.

  • (Score: 2) by MIRV888 on Saturday August 21 2021, @10:37AM (2 children)

    by MIRV888 (11376) on Saturday August 21 2021, @10:37AM (#1169260)

    Babylonians worshiped Baal and calculated triangles.
    Thus the lord god destroyed them.

    • (Score: 3, Funny) by kazzie on Saturday August 21 2021, @01:18PM

      by kazzie (5309) Subscriber Badge on Saturday August 21 2021, @01:18PM (#1169282)

      The carpenter's son wanted everyone to use a try square.

    • (Score: 0) by Anonymous Coward on Saturday August 21 2021, @10:56PM

      by Anonymous Coward on Saturday August 21 2021, @10:56PM (#1169419)

      Baal is a fairly reasonable system lord, but whatabout Hathor/Ishtar?

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