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OT: Babylonian trig table: nearly 4000 years old

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  • OT: Babylonian trig table: nearly 4000 years old

    "A 3,700-YEAR-old Babylonian clay tablet discovered by the real Indiana Jones has been revealed as the world's oldest - and most accurate - trigonometric table.
    ...

    The tablet was discovered in the early 1900s in what is now southern Iraq by archaeologist, diplomat and antiquities dealer Edgar Banks, the person on whom the fictional character Indiana Jones was based."

    http://www.express.co.uk/news/world/...-Indiana-Jones

  • #2
    Too bad they do not give examples of what the tablet says, instead of generalities of what it means , like building structures.
    I did have a chuckle when they said it had "ratios" of triangles ...that is exactly what Trig is...... RATIOS
    When I taught trig to our machinists at work, I had to get it in their heads , you are dealing with fractions and ratios...that is simple.
    Forget the mathematicians words like Secant, Co-secant etc, etc......think of fractions and it is much easier to learn than to wrap your brain with strange words.
    Rich

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    • #3
      Originally posted by Rich Carlstedt View Post
      Too bad they do not give examples of what the tablet says, instead of generalities of what it means , like building structures.
      I did have a chuckle when they said it had "ratios" of triangles ...that is exactly what Trig is...... RATIOS
      When I taught trig to our machinists at work, I had to get it in their heads , you are dealing with fractions and ratios...that is simple.
      Forget the mathematicians words like Secant, Co-secant etc, etc......think of fractions and it is much easier to learn than to wrap your brain with strange words.
      Rich
      The ratios all DO have names. The names are just a way to get into (or out of) the angle table when you have a ratio and need the angle, or have an angle and need the ratio.

      It's far from "PC" now, but I still remember the old "Indian" method. Chief Soh Cah Toa. Sine= Opposite/Hypotenuse Cosine=Adjacent/Hypotenuse Tangent=Opposite/Adjacent. All meaning the sides opposite etc to the angle you are working with.

      So if you have the ratio, then you can look at a table of Arctangent, arcsine etc (may be called "Inverse sine" or "Inverse tangent", etc), so you can get to the angle. If you have the angle, the sine, tangent, etc of the angle gives you the ratio.

      I assume the Babylonians did not get conderned with the angle, but directly used the ratios. It makes a good deal of sense, actually.
      1601

      Keep eye on ball.
      Hashim Khan

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      • #4
        I'm sure it's due to the need to appeal to a wide audience, but these light-weight fluff "science" articles leave more questions than they answer.

        Our home town news paper is like that. They obviously don't have a true science editor. The authors of "science" articles don't even know what questions to ask. Contrast this with bigger papers. NYT has at least one science editor who does a pretty good job getting past the pablum and into some good scientific inquiry.

        Ed
        For just a little more, you can do it yourself!

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        • #5
          Looking at the wiki page, Babylonian mathematics were pretty advanced, but I suspect that their trig table (if that's what it is) is not "the most accurate". After all, they approximated Pi as 3.

          Still, they did much better than I could do.

          Dan
          At the end of the project, there is a profound difference between spare parts and extra parts.

          Comment


          • #6
            Originally posted by danlb View Post
            Looking at the wiki page, Babylonian mathematics were pretty advanced, but I suspect that their trig table (if that's what it is) is not "the most accurate". After all, they approximated Pi as 3.

            Still, they did much better than I could do.

            Dan
            Maybe their tables were for easy ratios like sin(1/2) that is exactly 30 degrees and something that you can come up with pen and drawing paper?
            But just like ed_h said the articles leave more questions than it answer.

            Comment


            • #7
              http://www.abc.net.au/news/2017-08-2...matics/8841368
              "According to UNSW, Plimpton 322 is a trigonometric table that is the world's only completely accurate one, because it only includes Pythagorean triangles with side lengths that are whole numbers.

              "This ensures that the ratios of sides and squared ratios can be represented in the table without approximation," Dr Mansfield said."

              Why there is no plain-numbers translation of the table??
              Would make absolutely no sense to someone who is not used to base-60 system?

              Comment


              • #8
                So its about exact ratios that give 90-degree corner?
                3-4-5 is the most commonly known but there is also others in base-10 system like 5, 12, 13 and 7, 24, 25
                http://personal.maths.surrey.ac.uk/e...ag/pythag.html

                I don't want to think what they have in base-60

                Comment


                • #9
                  Leaves more questions.....
                  Did they use single place numbers all the way to 59? I guess it wouldn't matter if you use columns to separate the numbers in base 60.
                  Did 360 deg or 60 deg represent a full circle or was there some other way?
                  Did 1:15 represent 90 deg? How would 1:15 be presented in base 60?
                  Last edited by Abner; 08-25-2017, 08:15 AM.

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                  • #10
                    Ad far i understand the article - table contains list of right angled tringles with "round" side lenghts. Such table can be used to easily define angles that are easy to measure on construction site with very simple tools. You dont even need "right angle" - all you need is a stick (of any length) and some rope.
                    You cannot use it define any angle (for exaple 45 degrees is impossible) but these that can be defined will be very accurate.

                    Wysłane z mojego GT-N7100 przy użyciu Tapatalka

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                    • #11
                      Even the title of the article is misleading. A list of Pythagorean triples is not what most people think of as a "trig table".

                      Ed
                      For just a little more, you can do it yourself!

                      Comment


                      • #12
                        There is complicated trigonometry in the testing and correction of revenue metering potential and current transformers
                        to their actual burden impedance.
                        I suppose it is important for proof that the big companies are accurately billed for their electricity.

                        Calculations are to accuracy of milli-radians and/or minutes of angle.

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                        • #13
                          This should be straight "from the horse mouth"
                          http://www.sciencedirect.com/science...15086017300691

                          Comment


                          • #14
                            Originally posted by J Tiers View Post
                            It's far from "PC" now, but I still remember the old "Indian" method. Chief Soh Cah Toa. .
                            I used the same method for college trig back in 85.

                            Comment


                            • #15
                              Is not the use of division etc by 60 instead of our 50 not only similar to our clock but also very similar to our mathematical useage of division by minutes and seconds in engineering today. I t is similar to choice of metric to any other method. I personally was brought up like every child in Britain using imperial then in 1970-1971 we here in the UK converted our currency to metric awaiting our imminent joining the European community .I find the funny thing is we were imperial users changed to European and American coinage using metric which you guys had obviously preferred when you became free from us and set up on your own,however in maths you held onto for engineering measurement old and more difficult imperial. imho Alistair
                              Please excuse my typing as I have a form of parkinsons disease

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