• wonderingwanderer@sopuli.xyzEnglish
    8·
    5 hours ago

    Can someone explain the formula? Is it real? What does it do?

    I miss PugJesus :( he would usually explain these things

        • sparkyshocks@lemmy.zipEnglish
          1·
          9 minutes ago

          There are many different formulas for deriving digits of pi, and the history of mathematics has a bunch of people trying to brute force inefficient formulas for pi out to a few digits, as they develop more efficient methods.

          Archimedes drew a circle and put some polygons around the inner and outer limits to determine that it was somewhere between 22/7 and 223/71, accurate to within 2 digits. That general polygon method was used by Ptolemy to calculate out to 3 digits, and used by Chinese mathematician Zu Chongzhi to estimate pi at 355/113, accurate to 7 digits.

          The polygon method was very tedious, requiring many, many calculations in order to advance just a few digits.

          The Liebniz formula was a breakthrough (discovered by Indian mathematician Madhava of Sangamagrama), because discovering that pi/4 was equal to the infinite series 1 - 1/3 + 1/5 - 1/7 . . . meant that someone could calculate some number of digits accurately, and then continue the calculation in a way that reports what is known so far, and can continue down the line towards a more precise result. Still, by itself, it was a very slowly converging algorithm, requiring 5 billion terms just to get to 10 digits of accuracy. Mathematicians got to using other tricks (that, if I’m being honest, I don’t understand) to make it faster.

          Then Ramanujan discovered series that were rapidly converging (including the one in this meme) where although calculating each term might require a lot of calculations, it would spit out 8 digits for each term you fed it. It became the preferred method for calculating digits of pi, and when computers were developed, they were able to make use of that computational efficiency. It still remains the basis for how a computer will calculate a few million digits of pi.

  • Jankatarch@lemmy.worldEnglish
    3·
    4 hours ago

    I have solved a programming design problem in my sleep few times. Nowhere near PhD level problems tho.

  • turtlesareneat@piefed.caEnglish
    7·
    7 hours ago

    I’m still trying to figure out how it can be simultaneously nighttime and daytime in my dreams so mazel tov, you’re in the AP classes here

    (I think my brain doesn’t render rayleigh scattering)

  • Danitos@reddthat.comEnglish
    24·
    10 hours ago

    I’m 100% not joking, I once was stuck the the proof of a theorem for a whole week going at it and still wasn’t able to prove it… until I dreamed of the solution, woke up at like 3 am, quickly wrote a skecth of my dream’s proof and went back to sleep. The following morning I checked that path and boom, there it finally was the solution.

    Weirdly enough, this happened twice, although that second time I didn’t woke up at 3 am, just in the following morning as usual.

    • wonderingwanderer@sopuli.xyzEnglish
      6·
      5 hours ago

      I read somewhere that Mick Jagger (or maybe it was Keith Richard) wrote the riff of Satisfaction in his sleep.

      He woke up, grabbed a tape recorder and went “Bum bum. Bumbumbuummm bumbumbum.” And sang the one line “I, can’t, get noo, sat-tis-fac-tion.” And then went back to sleep.

      Forgot about it the next morning till they were at band practice and someone found the tape and played it.

      • [object Object]@lemmy.worldEnglish
        2·
        2 hours ago

        Thunder is encoding the percent-signs, that are used for the original encoding of the dash. Which of course bungles the url.

        Presumably it allows Thunder to open URLs with raw Unicode characters in them. But ironically, I’ve just tried to insert the same address here with the dash preserved, and Thunder converted it to percent-encoding when posting (or Lemmy did, but I doubt that).