/sci/ - Science & Math

[Anonymous No.6643321]

Is there a formula in maths or physics more elegant than Euler's identity?

[Anonymous No.6643331]

Yeah I believe that it is:

<div class="math">\oint\limits_{E} OP \, \mathrm{d}cum = LOTS OF FUCKING CUM SWALLOWED</div> where <span class="math">E[/spoiler] denotes the curve down the OP's esophagus.

[Anonymous No.6643332]

https://en.wikipedia.org/wiki/Tupper%27s_self-referential_formula

[Anonymous No.6643346]

>>6643321
Barnett's Identity

sum of k from k=0 to infinity = e^(iπ)/11.999...

/thread

[Anonymous No.6643355]

Anything that doesn’t require a filthy +1.

[Anonymous No.6643431]

>>6643321
<span class="math"> \displaystyle
e^{i \frac{\tau}{2}}+1=0
[/spoiler]
Absolute fap level material

[Anonymous No.6643444]

δS = 0

[Anonymous No.6643457]

>>6643321
>>6643346

Barnett's equality seconded.

[Anonymous No.6643462]

No, Barnett's identity is

<span class="math">\displaystyle \sum_{k\mathop = 0}^{\infty} k = \frac {e^{i \tau / 2}} {11.999 \ldots}<span class="math">[/spoiler][/spoiler]

[Anonymous No.6643490]

>>6643321
> e^(i*pi) = -1 is magical
e^(i*tau) = 1 ?

[Anonymous No.6643532]

>>6643462
Thanks for actually writing it correctly (with the tau)

[Anonymous No.6643538]

I don't think Euler's identity is all that great.

[Anonymous No.6643542]

>>6643431
fucking trolls...

[Anonymous No.6643544]

>>6643538
I didnt either until I turned 21. Then I realized that if you write the taylor series associated to exp, and look at what you get for i*tau/2...

[Anonymous No.6643552]

It's actually better if you leave the argument as a variable theta and write the e^(i*theta), cos(theta) and i*sin(theta) in terms of their taylor series expansions

[Anonymous No.6644804]

>>6643462
epeck mem summerfriend

[Anonymous No.6646636]

>>6643321

[Anonymous No.6646651]

n = (n-1) + 1

[Anonymous No.6646656]

E = m * (a^2 + b^2)

[Anonymous No.6646657]

Could someone explain to a math pleb what's so beautiful about Euler's Identity or the formula?

It just seems like yet another formula in math.

[Anonymous No.6646660]

>>6646657
There is nothing beautiful about it. It's just reddit teenagers who think having i and pi in the same equation makes it an epic event for "le math nerds". People who think like that are immediately revealing that their math education stopped somewhere in high school.

[Anonymous No.6646686]

>>6646660
This, these people don't stop and ask themselves "what the fuck does it mean to raise e to a complex exponent?" The answer to this question is the complex exponential function and from there the identity is completely trivial. It's kind of neat how the definition of the trig functions in terms of the exponential function corresponds, when restricted to the real line, to the usual trig functions, but that's hardly what I'd call "beautiful".

[Anonymous No.6646692]

>>6646657
<span class="math">i[/math, <span class="math">\pi[/spoiler], and <span class="math">e[/spoiler] have nothing to do with each other, yet when combined they make something fundamental. That's beautiful.[/spoiler]

[Anonymous No.6646694]

>>6646657
<span class="math">i[/spoiler], <span class="math">\pi[/spoiler], and <span class="math">e[/spoiler] have nothing to do with each other, yet when combined they make something fundamental. That's beautiful.

[Anonymous No.6646699]

>>6646694
Seems more trivial than anything. Less work of art, more parlor trick.

[Anonymous No.6646702]

>>6646699
This is what it is. The whole point of parlor tricks is to impress people who don't know any better, i.e. don't understand what exponentiation is in the context of complex analysis.

[Anonymous No.6646728]

>>6646694
The more elegant form is really: \displaystyle e^{i \tau}=1

[Anonymous No.6646733]

>>6646728
Tex works with [moth] [/moth] tags. math, not moth.

[Anonymous No.6646737]

>>6646733
Huh, testing this shit out: <span class="math">\displaystyle e^{i \tau2}=1[/spoiler]

[Anonymous No.6646739]

>>6646737
Shit, <span class="math">\displaystyle e^{i \tau}=1[/spoiler]

[Anonymous No.6646746]

>>6643346>>6643457
I laughed super hard.

[Anonymous No.6646751]

Schumacher's quantum source coding theorem and its resemblance to Shannon's classical source coding theorem.
The Gelfand-Naimark-Segal theorem.
The proof using inverse limit sequences that every compact metric space is the continuous image of the Cantor set.
The probabilistic proof of Weierstrass' approximation theorem.
The structure theorem for simple algebras.
The Central Limit Theorem.

If you want something you can post on reddit with zero effort and get lots of karma for, here's something really nice:
\int_{-\infty}^{\infty} e^{-x^2} \, dx = \sqrt{\pi}

>implying Euler's identity isn't completely trivial

[Anonymous No.6646769]

>>6646686
>these people don't stop and ask themselves "what the fuck does it mean to raise e to a complex exponent?"
You only know what it means either because you had DeMoivre's formula, Euler's formula, and/or the Taylor series expansion of the exponential, sine, and cosine functions taught to you, and in all likelihood had it shown to you how these can be used to derive Euler's identity.
Don't fucking act like you ever pondered the deeper meaning of a complex exponent. And, even if you did, it required some higher level background knowledge that Average Joe doesn't have access too.

>inb4 DeMoivre's formula, Euler's formula, and the Taylor series isn't higher level
You fucking know what I mean, don't be a prick.

[Anonymous No.6646787]

>>6646769
It's not about pondering any deeper meaning, it's about recognizing that a complex exponent is meaningless as far as "the Average Joe" is concerned, i.e. there's not any hand-wavy explanation in terms of repeated multiplication like the one that you can make sense of with real exponents. People are seeing an expression that looks very familiar and almost makes sense and ignoring the part that doesn't make so much sense.

[Anonymous No.6646812]

>>6646739
>2014
>Using Tau

[Anonymous No.6646813]

>>6646769
>>6646787
Also, I realize now that my post may have come off as judgmental, but it wasn't intended that way.

[Anonymous No.6646903]

>>6646657

There's a very long poster near the math department at my University talking about this formula. The short version of it is, (some) people find it fascinating that 4 of the most fundamental numbers (?) are the parts of this one formula. Then something about hawking or someone saying "We don't really understand what this means, but we can prove that it's true."

Most of the things I just said were probably partly wrong, but whatever I'm quoting from memory something I cannot possibly double check right now.

[Anonymous No.6646927]

>>6646657
Well, a way to see it is this:

This formula combines 2 of the most important transcendental numbers (that we know of), pi and e.

I also comb combines all of the basic operators, i.e. addition, multiplication, exposition. And equality.

And lastly, the neutral element of addition (0) and the neutral element of multiplication (1).

Other than that, it's a pretty trivial equality.

[Anonymous No.6647310]

1+1=2

[Anonymous No.6647312]

>>6643457
>>6643462
>>6643346
Someone should commit it to some journal4thelulz

[Anonymous No.6648342]

>>6646927
>>6646657

Its beautiful because rarely is e^(ikx) useful in the real world mathematics, eg calculating your bills and finances.

It is only useful when you delve into deep physics, where calculus is required.

And using e^(ikx) subsitution makes the calculus so MUCH EASIER.

[Anonymous No.6648511]

>>6646636
you didnt reduce

[Anonymous No.6648517]

>>6647310
1+1 = 10.

[Anonymous No.6649866]

>>6646927
>Equivalence is one of the, "four main operators"

Equivalence is a relation; a binary operator takes two arguments and maps them to an output.

>Neutral number

They are the identities of multiplication and addition...

[Anonymous No.6649916]

>>6646769
>You only know what it means either because you had DeMoivre's formula, Euler's formula, and/or the Taylor series expansion of the exponential, sine, and cosine functions taught to you
None of those explain what it means to raise a number to a complex exponent. The definition of complex exponentiation relies on defining "logarithm" functions which sort of act locally as an inverse for the complex exponential function and then further defining local "power" functions (using those "logarithms") which satisfy the usual power laws and are equivalent to the usual power operations when restricted to the reals.

Do you really think it's so absurd to think about what we mean by a complex exponent?
>>6649866
Ironic that "neutral element" is synonymous with "identity", but "equivalence" isn't "equality".

[Anonymous No.6649925]

>>6648517

1+1 = 0

le binary faec :^))))))))

[Anonymous No.6649959]

<span class="math">F+V-E=2[/spoiler]

[FTFY No.6649963]

>>6649925
1+1=1

[Anonymous No.6649968]

>>6643321
|G|=[G:H]|H| where H is a subgroup of finite G

[Anonymous No.6649995]

macrosopic maxwells equations for me.
they describe complicated interactions that determine our everyday life (any force we feel except gravity is electromagnetic in nature) in a simple, compact and symmetric way and lay the foundation for entire industries (optics, telecommunication, power etc).

[Anonymous No.6650001]

>>6649995
If you use Geometric algebra the equations reduce to <span class="math">\nabla F = J[/spoiler] which I think is much more elegant.

[Anonymous No.6650003]

>>6649995
>>6650001
Also there's:
<div class="math">\mathrm{d}F = 0</div>
<div class="math">\mathrm{d} \star F = \star J</div>

[Anonymous No.6650005]

>>6650001

never heard of this before, is there any good introduction to it?

[Anonymous No.6650009]

>>6650005
No, at least I don't think there's a good one. Right now I'm reading Electrodynamics: A modern geometric approach, by William Baylis. It's the best one that I've read.