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It seems so. According to https://worldhistorycommons.org/sumerian-school-days https://worldhistorycommons.org/sumerian-school-days: >This tablet, from ancient

It seems so. According to https://worldhistorycommons.org/sumerian-school-days https://worldhistorycommons.org/sumerian-school-days: >This tablet, from ancient Sumeria (as early as 2000 B.C.E.), details a day in the life of a school boy. Students learned by copying lessons on clay tablets, memorizing the lessons, and then reciting them for the school's headmaster (the "school father") or other teachers, monitors, and proctors of the school. This web page includes a full translation if you want to read it, and cites the paper "Schooldays: A Sumerian Composition Relating to the Education of a Scribe" (https://www.jstor.org/stable/596246 https://www.jstor.org/stable/596246) It makes sense that scribes would have formal education, like other highly-skilled professions imo, but I know nothing about history so who knows!

macrolime 4y ago
They also had formal education in ancient Egypt at the time. The math problems given to students at the time aren't trivial either. They need to do stuff like calculate the volume of various 3d shapes. Seems they used 256/81 (3.16) as an approximation of pi at the time. https://en.wikipedia.org/wiki/Moscow_Mathematical_Papyrus https://en.wikipedia.org/wiki/Moscow_Mathematical_Papyrus
- eru 4y ago
  That's an interesting approximation. The error is about 15 times larger than for the well-known 22/7 approximation.
  - macrolime 4y ago
    They supposedly got it by using an octagon to approximate a circle. Maybe that was a simpler approximation used in education, who knows.
  - mdp2021 4y ago
    According to Bruno Jarrosson, the Egyptians had a marked preference for some classes of fractions, e.g. those with unitary numerator (so that, for example, representing a quantity as a composition (e.g. sum) of more fractions of the form 1/n was preferred to using single fractions of the form m/n). So, that fraction may have been privileged over others in this framework. (One immediately notes that 256 and 81 are simple powers. As just a possibility, it could have been found intriguing that (2^8)/(3^4) could "reveal some underlying structure".)
    - eru 4y ago
      Yes, I was thinking about the simple powers, too. And I don't know whether they had enough math (or cared enough to do all the hard work with the math they had available to them), to figure out what's the simplest good approximation for the real value of Pi.
    - ben_w 4y ago
      Well spotted that they're simple powers; riffing on that idea, if that is the aesthetic behind it, I'd guess that they're supposed to be the same base or the same power, so either (4^4)/(3^4) or (16^2)/(9^2)? Edit: Or perhaps (((4^2)/(3^3))^2)^1 and then it feels like an ancient aesthetic-precursor to Euler's identity?
      - mdp2021 4y ago
        > the aesthetic behind it It could also have been practical: "Radius to circumference? Easy: double many times, then take thirds a few times".
        ben_w 4y ago
        Certainly feels plausible, that possibly makes a lot of sense.
        eru 4y ago
        Some more speculation. Have a look at https://en.wikipedia.org/wiki/Ancient_Egyptian_multiplication https://en.wikipedia.org/wiki/Ancient_Egyptian_multiplicatio... Egyption multiplication was (implicitly) based on powers of two. In some sense weirdly similar to modern bit-twiddling. Note that 4/3 in binary is 1.0101 0101 0101 0101 0101 0101 0101 0101... So that suggests the following algorithm, expressed in modern day Python: def mul4_3(x): table = [] while x > 0: table.append(x) x //= 4 return sum(table) I deliberately used a 'table', because that's what a scribe would do. Repeat this function four times, and you will have multiplied by 256/81. I have no clue whether they would have done anything resembling this procedure; this is just to show that it's plausible given how their multiplication worked. I don't know how this relates to 'Egyption fractions'. P.S. Just for fun the same thing for 22/7: def f22_7(x): y = (x << 1) + x while x > 0: x >>= 3 y += x return y Not actually harder to execute by hand, I'd say, but perhaps harder to come up with?
- SilasX 4y ago
  > 256/81 (3.16) Whoa, trippy coincidence. (16/3)^4 ~= 3.16
  - yifanl 4y ago
    Despite the math typo, (4/3)**4 is a pretty interesting composition of pi, if only because you get such a fundamental constant out of a relatively simple arrangement of low natural numbers.
  - SketchySeaBeast 4y ago
    I must be misunderstanding something, because based upon my understanding (16/3)^4 ~= (5.333)^4 (or 65536/81) ~= 809.
    - loudmax 4y ago
      16^4 / 3^4 = 256 / 81 That is interesting. Not as close to pi as the 22/7 that we were taught in middle school but maybe those exponentials were more meaningful to the Egyptians.
      - SketchySeaBeast 4y ago
        16^4 is not 256. 16^2 is 256. 16^4 is 65,536.
        SilasX 4y ago
        Oops, sorry.

macrolime 4y ago

They also had formal education in ancient Egypt at the time. The math problems given to students at the time aren't trivial either. They need to do stuff like calculate the volume of various 3d shapes. Seems they used 256/81 (3.16) as an approximation of pi at the time. https://en.wikipedia.org/wiki/Moscow_Mathematical_Papyrus https://en.wikipedia.org/wiki/Moscow_Mathematical_Papyrus

eru 4y ago
That's an interesting approximation. The error is about 15 times larger than for the well-known 22/7 approximation.
- macrolime 4y ago
  They supposedly got it by using an octagon to approximate a circle. Maybe that was a simpler approximation used in education, who knows.
- mdp2021 4y ago
  According to Bruno Jarrosson, the Egyptians had a marked preference for some classes of fractions, e.g. those with unitary numerator (so that, for example, representing a quantity as a composition (e.g. sum) of more fractions of the form 1/n was preferred to using single fractions of the form m/n). So, that fraction may have been privileged over others in this framework. (One immediately notes that 256 and 81 are simple powers. As just a possibility, it could have been found intriguing that (2^8)/(3^4) could "reveal some underlying structure".)
  - eru 4y ago
    Yes, I was thinking about the simple powers, too. And I don't know whether they had enough math (or cared enough to do all the hard work with the math they had available to them), to figure out what's the simplest good approximation for the real value of Pi.
  - ben_w 4y ago
    Well spotted that they're simple powers; riffing on that idea, if that is the aesthetic behind it, I'd guess that they're supposed to be the same base or the same power, so either (4^4)/(3^4) or (16^2)/(9^2)? Edit: Or perhaps (((4^2)/(3^3))^2)^1 and then it feels like an ancient aesthetic-precursor to Euler's identity?
    - mdp2021 4y ago
      > the aesthetic behind it It could also have been practical: "Radius to circumference? Easy: double many times, then take thirds a few times".
      - ben_w 4y ago
        Certainly feels plausible, that possibly makes a lot of sense.
      - eru 4y ago
        Some more speculation. Have a look at https://en.wikipedia.org/wiki/Ancient_Egyptian_multiplication https://en.wikipedia.org/wiki/Ancient_Egyptian_multiplicatio... Egyption multiplication was (implicitly) based on powers of two. In some sense weirdly similar to modern bit-twiddling. Note that 4/3 in binary is 1.0101 0101 0101 0101 0101 0101 0101 0101... So that suggests the following algorithm, expressed in modern day Python: def mul4_3(x): table = [] while x > 0: table.append(x) x //= 4 return sum(table) I deliberately used a 'table', because that's what a scribe would do. Repeat this function four times, and you will have multiplied by 256/81. I have no clue whether they would have done anything resembling this procedure; this is just to show that it's plausible given how their multiplication worked. I don't know how this relates to 'Egyption fractions'. P.S. Just for fun the same thing for 22/7: def f22_7(x): y = (x << 1) + x while x > 0: x >>= 3 y += x return y Not actually harder to execute by hand, I'd say, but perhaps harder to come up with?
SilasX 4y ago
> 256/81 (3.16) Whoa, trippy coincidence. (16/3)^4 ~= 3.16
- yifanl 4y ago
  Despite the math typo, (4/3)**4 is a pretty interesting composition of pi, if only because you get such a fundamental constant out of a relatively simple arrangement of low natural numbers.
- SketchySeaBeast 4y ago
  I must be misunderstanding something, because based upon my understanding (16/3)^4 ~= (5.333)^4 (or 65536/81) ~= 809.
  - loudmax 4y ago
    16^4 / 3^4 = 256 / 81 That is interesting. Not as close to pi as the 22/7 that we were taught in middle school but maybe those exponentials were more meaningful to the Egyptians.
    - SketchySeaBeast 4y ago
      16^4 is not 256. 16^2 is 256. 16^4 is 65,536.
      - SilasX 4y ago
        Oops, sorry.