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Submitted ⁨⁨7⁩ ⁨months⁩ ago⁩ by ⁨fossilesque@mander.xyz⁩ to ⁨science_memes@mander.xyz⁩

https://mander.xyz/pictrs/image/01bd60ca-3722-4672-88e6-ecfc3c2bcc2e.png

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Comments

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  • MarcomachtKuchen@feddit.org ⁨7⁩ ⁨months⁩ ago

    I’m allways astonished by how many function seemingly have nothing to do with circles and yet somehow a pi managed to snuck itself in

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    • NeatNit@discuss.tchncs.de ⁨7⁩ ⁨months⁩ ago

      Usually when that happens there’s a way to tie it back to circles, but it’s not always easy to find

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      • notabot@lemm.ee ⁨7⁩ ⁨months⁩ ago

        You could say you just go round and round hunting for it, but no matter how hard you try you just can’t corner it.

        Well, you could.

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      • xantoxis@lemmy.world ⁨7⁩ ⁨months⁩ ago

        there’s a way to tie it back to circles

        Not necessarily circles, but conic sections. When you take a series of a fixed exponent over a variable x, and graph it, that graph is a parabola.

        A parabola is a slice through a cone. Tada, pi appears.

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    • Didros@beehaw.org ⁨7⁩ ⁨months⁩ ago

      It makes sense if you consider that mass without outside forces forms a sphere. If you have enough atoms you get a sphere, and if you only have two they will circle eachother. Two hydrogen atoms are two spheres of neutrons and protons being circled by an electron circling eachother. It’s circles all tge way down.

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  • grubberfly@mander.xyz ⁨7⁩ ⁨months⁩ ago

    tbf, the 2nd sum is exactly the first one just multiplied by 1/2. though i get that the progression is natural, even, and odd.

    the last one is definitely odd puzzling, but i cannot intuitively get the first one. how does summing the inverse of triangular number equal 2?

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    • BugleFingers@lemmy.world ⁨7⁩ ⁨months⁩ ago

      I believe starting with 1/1 which equals 1, you are then adding infinitely (fractions) on top of the 1. So 1, then 1 1/2, ect, so the next full integer to be hit (infinitely down the line) would be 2.

      I don’t do high level math so I hope this explanation is correct or intelligible, this is just how I understand it intuitively

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      • yetAnotherUser@discuss.tchncs.de ⁨7⁩ ⁨months⁩ ago

        But the first few values are:

        1 + 1/3 + 1/6 + 1/10 + 1/15 + 1/21 + 1/28…

        I really don’t see any pattern there showing why it converges to 2 exactly

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        • -> View More Comments
    • lolcatnip@reddthat.com ⁨7⁩ ⁨months⁩ ago

      It’s not saying the proof is obvious, just that the result is plausible on its face.

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    • Collatz_problem@hexbear.net ⁨7⁩ ⁨months⁩ ago

      1/(n * (n+1)) = 1/n - 1/(n+1)

      1/(12) + 1/(23) + 1/(3*4) + … = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + … = 1

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      • AernaLingus@hexbear.net ⁨7⁩ ⁨months⁩ ago

        Written a bit more explicitly (although I kinda handwaved away the final term–the point is that you end up with one unpaired term which goes to zero)

        Image

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  • mkwt@lemmy.world ⁨7⁩ ⁨months⁩ ago

    1 + 2 + 3 + 4 + 5 + … = -1/12

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    • PlexSheep@infosec.pub ⁨7⁩ ⁨months⁩ ago

      Under very special circumstances an argument can be made for this, at least

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      • lolcatnip@reddthat.com ⁨7⁩ ⁨months⁩ ago

        Not really. The left side comes from trying to evaluate the Reimann zeta function at a point outside its domain, and the right side comes from evaluating the analytic continuation of the zeta function at the same point. The deepest truth it reveals is that applying the definition of a function outside its domain can give you nonsense results.

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      • Tudsamfa@lemmy.world ⁨7⁩ ⁨months⁩ ago

        Never understood those circumstances, but I choose to believe that all even numbers summed are therefore -2/12 and all odd numbers therefore 1/12.

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    • wewbull@feddit.uk ⁨7⁩ ⁨months⁩ ago

      That’s where I assumed it was going.

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  • jeffhykin@lemm.ee ⁨7⁩ ⁨months⁩ ago

    What’s the big deal? Just solve for …

    … = (π^2 / 6) - (1 + 1/4 + 1/9)

    Ez

    /s

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  • 4oreman@lemy.lol ⁨7⁩ ⁨months⁩ ago

    how dare you post math in this sub

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  • Th3D3k0y@lemmy.world ⁨7⁩ ⁨months⁩ ago

    Yeah, but is the function for 1 over odd numbers, or 1 over prime numbers …

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    • GreatRam@lemmy.world ⁨7⁩ ⁨months⁩ ago

      1 isn’t a prime number

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      • kryptonianCodeMonkey@lemmy.world ⁨7⁩ ⁨months⁩ ago

        And 2 is.

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  • PenisDuckCuck9001@lemmynsfw.com ⁨7⁩ ⁨months⁩ ago

    Tired of waiting 2 seconds for hyperpi to download? Do this instead. Thanks, internet!

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