• 101 Posts
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Joined 2 years ago
Cake day: June 6th, 2023
  • tetris11@lemmy.mltoComic Strips@lemmy.world•Good Cop/Bad Cop (Buying a Car)
    39·
    1 day ago

    blondie: “your colleague ratted on you, said you were selling these for high margins.”

    manager: “h-he said that?”

    blondie: “he practically sang, and now he’s dead. We can put it all on him and call it a day, or I can tell the feds that you were the mastermind behind the whole show.”

    manager: *sweats*

    blue shirt: “w-we just… we just need a price. Please.”

  • tetris11@lemmy.mltoPeople Twitter@sh.itjust.works•Pretty low standards
    32·
    11 days ago

    The lyrics of the rest of the song aren’t that great

     Strapped in the chair of the city's gas chamber
     Why I'm here, I can't quite remember
The Surgeon General says it's hazardous to breathe
           I'd have another cigarette
But I can't see, tell me who you're gonna believe

        Take me down to the Paradise City
Where the grass is green and the girls are pretty

    So either the chorus is pure sarcasm, or his day to day to life is so unbearable that he genuinely wishes to go back to a time/place where the grass is green, and a time when he was still attracted to women

  • tetris11@lemmy.mltoScience Memes@mander.xyz•TIL science has its own swiftiesEnglish
    9·
    27 days ago

    For (1), we started with the Maclaurin series 1/x to get us familiar with the idea of differential expansions, and then we moved to Taylor to derive expansions of some common functions like cos and sin:

    cos(x) = 1 - x2/2! + x4/4! - …
    sin(x) = x - x3/3! + x5/5! - …

    We now start with the definition of ex Taylor expansion, and proceed to do some substitutions:

    ex = 1 + x + x2/2! + x3/3! + … + xn/n!

    We can then substitute in: x=iθ (remembering that i2 = -1) to get

    eiθ = 1 + iθ - θ2/2! - iθ3/3! + θ4/4! + iθ5/5! + … etc…

    If we group by real and complex, we can arrange the above as:

    eiθ = (1 - θ2/2! + θ4/4! + … ) + i(θ - θ3/3! + θ5/5! + … )

    You should now realise that the left part resembles the expansion of cos(θ), and the right part resembles sin(θ). That is:

    eiθ = cos(θ) + i sin(θ)

    Finally, we substitute in θ = π

    eiπ = cos(π) + i sin(π)

    And we know that cos(π) = -1, and that sin(π) = 0, meaning that we end up with

    eiπ = -1 + i 0

    or

    eiπ + 1 = 0

    The teacher got excited because it is literally one of the most beautiful mathematical statements you can get, that connects five universal identities under a single statement: 0, 1, e, i, and π – and does so using 3 different operators (times, power, plus).

    For (2), I’m still waiting as I think it’s currently holding the world together by sheer mass alone

  • tetris11@lemmy.mltoScience Memes@mander.xyz•TIL science has its own swiftiesEnglish
    321·
    27 days ago

    My high school teacher introduced this to us as a slow reveal over the course of weeks of what would be the proof of

    eiπ = -1

    The happiest moment was when he brought in these two disparate field of mathematics, complex numbers and series expansions, and hit us with this magnificent revelation. Once he drew it up, he stood there shaking with excitement, beaming at us at how amazing this all was.

    The class wasn’t having it. We were teenagers. We understood it from a purely proof level, but did not get the implications. It was years years later that it all hit me how amazingly neat it was of the universe to unite these fields together like that and to unearth literally new tools we could use to explore further fields of maths.

    Thankfully since then I’ve started dating Taylor Swift and reading the words of Samule Taylor Coleridge, whilst getting clothes fitted to size at my local clothes-maker guy to fit my enourmous expanding schwang.