/sci/ - Science & Math

>>12463463
[math]e^{180i}+1=0[/math]

>muh beauty and elegance

You can replace pi with whatever convention you use to represent a half turn. It is entirely arbitrary.

>>12463463
Convince yourself that the archimedean principle is true and maybe we can talk later you dumb fuck

the real numbers are a disgrace to rigor in mathematics

>>12463463
>why does everyone hail this equation as biblical ?
who is "everyone"?

>>12463463
Its a fancy way of saying that if you walk half the way around the garden and then half the way across the garden you will be in the middle of the garden.

>>12463487
https://www.livescience.com/51399-eulers-identity.html#:~:text=Euler's%20identity%20is%20an%20equality,called%20in%20his%20lectures%20%22our

wildberger pls leave

>>12463468
e^(180 * i) =
-0.598460069 - 0.801152636 i

>>12463475
hello tooker

>>12463463
This equation is the pleb filter

>>12463468
No

>>12463463
^
literally notational abuse.
if it can be described with an arithmetic algorithm it's fucking gay.

>>12463475
hello rigor freak

>>12463475
Based.
>>12463618
Tooker is a big supporter of real numbers.

>>12463463
I like it. Calculus, geometry, analysis come together in a neat little relation.

>>12463463
Imagine being like this, calling everything you don't understand a sign of schizophrenia

>>12463475
acc based

>>12463475
Delete your account

It lost much of its magical quality for me after I'd understood its derivation.

>>12463468
pi radians is a number, 180 degrees is not a number

>>12463999
Trips wasted.

>>12463992
It follows trivially from Euler's formula. Understanding that derivation is a little more insightful.

>>12464013
Euler's formula also follows trivially from the definition of sin and cos - whose definitions are derived from Euler's formula. Everything to do with the circle has a circular definition.

>>12464013
Yes, I mean the full derivation with Euler's formula as a step, not just plugging π into Euler's formula.

>>12463475
/thread

>>12464029
"All points that are equidistant from some fixed point" is not a circular definition.

>>12464029
That's why it's better to define sin and cos by their series representations. Euler's formula follows non circularly.

>>12463475
Denying the real numbers is the actual disgrace to rigor as you are rejecting completely rigorously defined and explored sets of numbers just because you can't conceptualize things like infinity or completeness.

>>12464052
cope more infinitist schizo

>>12464049
most geometric way to define sin and cos is probably by differential equations

>>12464052
>rigorously defined
Should we tell him?

>>12464056

>>12464066
That he's absolutely correct, and only gibbering retards and trolls disagree? I'm sure he knows.

>>12463463
You do realize that "thing I don't understand because I'm dumb or didn't do any research" is NOT the same as "this thing is schizoid nonsense"?

>>12464146
>only gibbering retards and trolls disagree

>>12464043
[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]

>>12464166
>Needs a quote literally over a century old to prove his point
Wow. Are you going to bring up Napoleon saying that steam powered ships are impossible? Or IBM saying there's only a market for a few thousand computers?

>>12464168
Huh. Cool

>>12464290

>>12464011
nah, theyre just simply correct

>>12464168
Based proof technique 10/10