/sci/ - Science & Math

[Anonymous No.10902942]

wow.. this really makes you think

[Anonymous No.10902943]

that picture really made me think

[Anonymous No.10902947]

[math] \displaystyle
f(x) = e^{-ix}(\cos x + i \sin x)
\\
f^{\prime}(x) = e^{-i x}(i \cos x - \sin x) - i e^{-i x}(\cos x + i \sin x)
\\
f^{\prime}(x) = e^{-i x}(i \cos x - \sin x) - e^{-i x}(i \cos x + i^2 \sin x) \equiv 0
\\
f^{\prime}(x) = 0 \;\;\; \forall \; x \in \mathbb{R}\Rightarrow f(x) \text{ is a constant}
\\
f(0) = e^{0}(\cos 0 + i \sin 0) = 1 \cdot(1+0) = 1 \Rightarrow f(x) = 1 \;\;\; \forall \; x \in \mathbb{R}
\\ \\
1 = e^{-ix}(\cos x + i \sin x) \Rightarrow e^{ix}=\cos x + i \sin x \;\;\; \forall \; x \in \mathbb{R}
[/math]

[Anonymous No.10902950]

if you were abducted by aliens and they said “you will die if you do not present to us the most beautiful equation in the whole universe, earthling desu” you would just show them this and they would have to let you go.

[Anonymous No.10902971]

>>10902942
>if you turn halfway around... you'll be facing the other way!
>woah... duuude. Such equation. Very math.
It looks cute, sure, but all the interesting insight comes well beforehand. I'm tired of this being shilled to normies like it's some kind of grand mystical statement.

[Anonymous No.10902975]

>>10902971
what? dude its the most beautiful equation ever it has exponentiation, addition, multiplication plus the e number, i, pi, 1, zero and the equals sign! some people can’t appreciate beauty i guess

[Anonymous No.10902977]

>>10902942
>Filthy human, what is e? If you are going to use constants then write all of their digits. What's that? You still have not developed a complete theory of complex analysis on the rationals? This means your species does not even have the intelligence to be sentient. Xiepthblorg, Call the ethics committee, it's okay to kill and farm these tall cows.

[Anonymous No.10902981]

>>10902977
>he used sentient when he meant sapient like a dumb normalfag
had to ruin it didn’t you?

[Anonymous No.10902985]

>>10902950
>most beautiful equation
>not [math]\int _M d \omega = \int _{\partial M} \omega[/math]

[Anonymous No.10902987]

>>10902975
Ideas are beautiful. Their representations are kitsch at best.

[Anonymous No.10903003]

>>10902975
Personally I prefer the full form where the RHS is multiplied by [math] \frac{\phi}{2} [/math]

[Anonymous No.10903012]

>>10902977
>aliens would have less developed mathematics
Nope, if anything aline would have a number system even beyond real numbers, that would make Wildberger seethe

[Anonymous No.10903015]

>>10903012
3000 IQ aliens do all math on the algebraic closure of the rationals, and they have constructive proofs of FTA via induction.

[Anonymous No.10903019]

>>10902977
>a complete theory
Anon...

[Anonymous No.10903069]

>>10902950
Technically, that's not an equation, but an identity.
acshually_nerd.png

[Anonymous No.10903073]

>>10902975
there's no 1728 though

[Anonymous No.10903089]

>>10902942
Why bother adding 1 to make it equal to zero? Just let it be equal to -1.

[Anonymous No.10903109]

>>10903089
the appereance of 0 is part of the "beauty"

[Anonymous No.10904559]

>>10902947
no proof, you have not shown that the solution to a cauchy problem is unique. there may be many such f satisfying the proposed ODE.

[Anonymous No.10904563]

>>10903069
lol faggot

[Anonymous No.10904567]

>>10903069
typical highschool math student right here.

[Anonymous No.10904586]

>>10903089
The idea is that the most important, beautiful, or even most common numbers in mathematics appear in this one equation: e, i, pi, 1, and 0.

[Anonymous No.10904614]

>>10902942
What level of math do you need to know for this to make sense anyways?

[Anonymous No.10904629]

>>10904563
>faggot
Why the homophobia?

[Anonymous No.10905069]

>>10904559
what ode, where

[Anonymous No.10905100]

>>10904614
do you know taylor series?

[Anonymous No.10905107]

>>10904614
[math] \displaystyle
e=\frac{1}{0!}+\frac{1}{1!}+\frac{1}{2!}+\frac{1}{3!}+\frac{1}{4!}+\cdots
\\ \\
e^x=\frac{x^0}{0!}+\frac{x^1}{1!}+\frac{x^2}{2!}+\frac{x^3}{3!}+\frac{x^4}{4!}+\cdots
\\ \\
sin(x)=\frac{x^1}{1!}-\frac{x^3}{3!}+\frac{x^5}{5!}-\frac{x^7}{7!}+\frac{x^9}{9!}-\cdots
\\ \\
cos(x)=\frac{x^0}{0!}-\frac{x^2}{2!}+\frac{x^4}{4!}-\frac{x^6}{6!}+\frac{x^8}{8!}-\cdots
\\ \\
cos(x)+sin(x)=1+x-\frac{x^2}{2!}-\frac{x^3}{3!}+\frac{x^4}{4!}+\frac{x^5}{5!}-\frac{x^6}{6!}-\frac{x^7}{7!}+\frac{x^8}{8!}+\frac{x^9}{9!}-\cdots
\\ \\
e^{ix}=\frac{(ix)^0}{0!}+\frac{(ix)^1}{1!}+\frac{(ix)^2}{2!}+\frac{(ix)^3}{3!}+\frac{(ix)^4}{4!}+\cdots
\\ \\
e^{ix}=1+ix-\frac{x^2}{2!}-\frac{ix^3}{3!}+\frac{x^4}{4!}+\frac{ix^5}{5!}-\frac{x^6}{6!}-\frac{ix^7}{7!}+\frac{x^8}{8!}+\frac{ix^9}{9!}-\cdots
\\ \\
e^{ix}=\left ( 1-\frac{x^2}{2!}+\frac{x^4}{4!}-\frac{x^6}{6!}+\frac{x^8}{8!}-\cdots \right )
+i \left ( x-\frac{x^3}{3!}+\frac{x^5}{5!}-\frac{x^7}{7!}+\frac{x^9}{9!}-\cdots \right )
\\ \\
e^{ix}=cos(x)+i \, sin(x)
[/math]

[Anonymous No.10905112]

>>10905100
Of course, I love "Shake It Off"

[Anonymous No.10905114]

>>10905107
you uh fucked up your Ga(y)TeX my very undergraduate friend

[Anonymous No.10905118]

>>10905112
well the easiest proof is taylor series
and if you understand what imaginary numbers are, you can prove it pretty easily

so I would say you need introductory calculus

[Anonymous No.10905159]

>>10905114
[citation needed]

[Anonymous No.10905162]

>>10905107
***[math]\exp(j\theta)=\cos(\theta)+j\sin(\theta[/math]
ftfy

[Anonymous No.10905167]

>>10905159
the hideous mess above is improper Ga(y)TeX its very clear that's exactly what you intended to make use of and you failed in doing so. You could just repost it instead of being a passive aggressive little insect.

[Anonymous No.10905168]

>>10905167
>>10905159

[Anonymous No.10905240]

>>10905167
retard rage

[Anonymous No.10905259]

>>10905240
r u mad?

[Anonymous No.10905267]

>>10905259
>projecting

[Anonymous No.10905287]

>>10902947

This is a horrible proof. It only works because you already know the result, it doesn't actually show anything.

[Anonymous No.10905293]

>>10905107

missing the proof that you are even allowed to write e^x , cos x , sin x as a power series aka that they are differentiable continuously

i guess theres ojnly undergrads in here lmao