• too_high_for_this@lemmy.world
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        6 hours ago

        For real though:

        Decimal representation of pi is 3100+1*10-1+410^-2

        So each digit represents a power of 10. Base pi works the same, kinda. 1 in base pi = 1pi^0, 10 = 1pi, 20 = 2*pi, etc.

        This is the best I can do right now, I’m

    • 🍉 DrRedOctopus 🐙🍉@lemmy.world
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      11 hours ago

      how the fuck i didn’t realize that!!!

      Fuck,

      so 1 in base pi is still 1, but 10 is pi

      makes sense,

      1 =pi ^ 0

      10=pi^1

      100 = pi^2

      my intuition kept telling me that using an irrational base system would end up with all integers being irrational. didn’t realize how easy it is to prove it otherwise

      ie, I had a very bad conjecture and I gained better understanding why it was wrong

        • setsubyou@lemmy.world
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          7 hours ago

          1 in base 10 isn’t 1/10 and in hexadecimal it’s not 1/16.

          Decimal integers in base pi are 1, 2, 3, 10.2201…, 11.2201…, 12.2201…, 20.2201… and so on.

          Basically: 10.2201… = 1 * pi^1 + 0 * pi^0 + 2 * pi^-1 + 2 * pi^-2 … which approaches 4 as you add digits.

          But 1 is just 1*pi^0