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/sci/ - Science & Math

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6508711 No.6508711 [Reply] [Original]

what is the most beautiful, aethetically pleasing equation that equates the most in the least amount of symbols and formulation?

inb4 e=mc^2. that's too easy.

>> No.6508716
File: 10 KB, 199x187, Such beauty.png [View same] [iqdb] [saucenao] [google]
6508716

>>6508711
Easily these

>> No.6508717

<div class="math"> \int_{\Omega} d\omega = \int_{\partial \Omega} \omega</div>

>> No.6508720

>>6508716
then why not write them in the more compact form?

dF = 0
*d*F=J

>> No.6508721

F=ma

Equally boring answer, but true.

>> No.6508723

>>6508721
thats not even true in most cases, at least use F = dP/dt which is always correct. even if force its just a trivial definition no one uses outside of high-school

>> No.6508730

>>6508721

<span class="math"> \int F\cdot dt = \Delta p [/spoiler]

>> No.6508734

the statement of noether's theorem is the most beautiful thing of physics

>> No.6508765

>>6508720
I honestly don't know why I didn't do that, they are in a way much more beautiful.

>> No.6508771

A = BC

Where A is everything, B is everything else, and C is complex function.

>> No.6508773

e^{i \pi} + 1 = 0

>> No.6508776

>>6508734
stop whiteknighting you faggot

>> No.6508777

>>6508773
this

>> No.6508799

>>6508720
The second should be <span class="math">d \star F = J \mu_0.[/spoiler].
Even without any current, you overdid the duals! I agree with the fact they're beautiful equations.
I like index theorem; <span class="math">Index(D) = TopIndex(D)[/spoiler].
Defining Index(D) is easy, but the topological index requires some algebraic topology - just topological K-theory.

>> No.6508806
File: 113 KB, 960x648, 0.jpg [View same] [iqdb] [saucenao] [google]
6508806

Can't believe nobody has mentioned the mother of all equations
<div class="math">\delta S=0</div>

>equates the most in the least amount of symbols and formulation?
From this little equation you get basically the entire standard model of physics.
You can derive Newton's laws, electromagnetism, quantum mechanics, quantum field theory
^^ those are the ones I've seen, but I think I've also heard that it might be possible to get thermodynamics, relativity, and maybe even a little bit of string theory from it too

>> No.6508807

>>6508799
im sure ive seen them with 2 duels before.

could it be a different definition of J?

>> No.6508813

>>6508806
>QFT
no you cant, it would make more sense if you said
<span class="math"> \int Dq e^{iS} [/spoiler] is the mother since <span class="math"> \delta S = 0 [/spoiler] can be derived by taking the classical limit.

and if you mean general relativity, yes you can get it as well.

>> No.6508826

>>6508813
whoa really? This changes everything

>> No.6508845

>>6508773
Who in their right mind leaves that isolated 0 on the right side of the equation?

>> No.6508850

>>6508845
If you leave the isolated zero you use the five most important constants in math in one equation

>> No.6508853
File: 18 KB, 268x265, 1398680037433.jpg [View same] [iqdb] [saucenao] [google]
6508853

>>6508850
How about <div class="math">e^{i \pi} + 1 = 2*0 + 3*0 + 4*0 + ...</div>?!
It contains every number!

>> No.6508856

>>6508853
I lol'd

>> No.6508857

>>6508853
mathematics generally doesn't care about integers greater than 1

>> No.6508958

>>6508850
-1 Is important to. I propose:
e^(tau*i)+(-1)*(1)=0
Perfect!

>> No.6508961

1+2+3+...=-1/12

>> No.6508965

>>6508961
are you proud of yourself

>> No.6508973

a^2+b^2=c^2

where a and b are two sides of a right triangle and c is the hypotenuse

>> No.6508974

>>6508711

>inb4 e=mc^2. that's too easy

but that's the answer to your question dummy

>> No.6508978

<span class="math">dF=0
d \ast F = J[/spoiler]

or

<span class="math">\nabla_{\mu}F^{\mu \nu} = j^{\nu}
\nabla_{\mu}\widetilde{F}^{\mu \nu} = 0[/spoiler]

or

<span class="math">\delta \int d^4x F^{\mu\nu}F_{\mu\nu} = 0[/spoiler]

>> No.6508984

>implying it's not automatically e^ipi+1=0
>inb4 why no latex

>> No.6508999

0.999... = 1

This equation reveals the true beauty of math.

>> No.6509010

>>6508961
I keep getting the feeling we could get other weird answers to this.

>> No.6509011

>>6508999
>This equation reveals the true nature of /sci/
FTFY

>> No.6509014

final grade = 70/100

The only equation I need to succeed

>> No.6509015

>>6509010
because you can.. it's total bs

In pure math it is actually an incorrect statement.
People write it that way because in certain specific areas of physics replacing that sum with -1/12 is acceptable, but it's still an abuse of notation

>> No.6509018

alpha male index = number of girls you fucked / your age

>> No.6509022

>>6508974
>>>/mlp/

>> No.6509027

>>6508999
>those trips

wh-hhat

>> No.6509037

>>6508806
what does it mean

help a pleb psychology out

>> No.6509040

>>6509037
psychologist*

>> No.6509047

>>6508999
>digits
Wow. Considering how much that's posted on /sci/ it might not be as unlikely as I think it is.

>> No.6509054
File: 5 KB, 200x171, 1351547165932.jpg [View same] [iqdb] [saucenao] [google]
6509054

>>6508999

>> No.6509056

>>6509015
are you a fucking idiot? its in pure math that this sum was first done. physicists didnt use it until 100 years after that.

>> No.6509072

>>6509037
>>6509040
Look up principle of stationary action. In layman's terms, there's a certain quantity called the action, which is always stationary (i.e. the first derivative is zero) for the path that happens in nature. The quantity itself can be calculated by integrating the Lagrangian over the path.

>> No.6509079

Wood = (3/2)nK(Tree)

>> No.6509080

>>6508711
>what is the most beautiful, aethetically pleasing equation that equates the most in the least amount of symbols and formulation?

OP=FAG
have some eternal charm to it.

>> No.6509081

>>6508711
Oiler's formula:
1^pi+-1=0

>> No.6509088

>>6509080
>>>/b/

>> No.6509101

Euler's identity is pretty sweet
<div class="math">e^{ipi}+1=0</div>

Feynman called it the jewel of mathematics

>> No.6509104

>>6509056
0/10

it's a divergent series, undergraduate students learn this.. don't embarrass yourself

>> No.6509105

>>6509101
Sorry, don't know how to LaTeX yet

>> No.6509110

6/2(1+2) = 1

>> No.6509111

>>6509105
pi = \pi
you are no longer allowed to make mistakes

>> No.6509115

>>6509111
Thaanks, much appreciated

>> No.6509118

1=1

The most profound equation.
Reality is a tautology.
Math is too.
Interpretation systems such as life are pattern translating machines to approximate the tautology effectively enough to survive and reproduce.

>> No.6509125

>>6508973
It irritates me that people are still using Pythagoras' theorem for right triangle length, when if you want to find the third side of a triangle there's something called the law of cosines that does it for you much better. What the PT is most useful for is calculating area of similar shapes, ugh here's a link http://betterexplained.com/articles/surprising-uses-of-the-pythagorean-theorem/

>> No.6509135

>>6508711
>>6509125
(E)^2 = (mc^2)^2 + (pc)^2 is the greatest

>> No.6509157

>>6509125
cosine law is for fuckin faggots. no one gives a shit about non right triangles

>> No.6509419

>>6509118
You actually just blew my mind.

>> No.6509454

>>6508717
follows from <span class="math"> d^2 \omega = 0 [/spoiler]

>> No.6509459

>>6508999
mind=/b/lown

>> No.6509464

>>6508711
^ E 2=+ ^ * m ^ c 2 2 ^ * p c 2

>> No.6509470
File: 7 KB, 212x209, Maxwell equations up to the first order.png [View same] [iqdb] [saucenao] [google]
6509470

>>6508716
>No equation of motion making those equations worthless
>No symmetry

0/100

>> No.6509473

>>6509157
THIS

>> No.6509475

>>6508776
What do you mean?

>> No.6509479
File: 543 B, 140x18, 3213a84c042c6ecb7fbf51f89bedbd10.png [View same] [iqdb] [saucenao] [google]
6509479

I have always liked the formula for thermal radiation

>> No.6509484

<span class="math"> \mathbf{ \ddot{x}} = \mathbf{f} (t, \mathbf{x}, \mathbf{ \dot{x}} ) [/spoiler]

>> No.6509507

>>6509470
> magnetic monopoles
> no index notation to account for GM
> can't explain Aharonov-Bohm effect
> no classical phenomena

2/10 you tried.

>> No.6509529

>>6509104
YOU MAKE HULK MAD. THAT ANON DIDN'T DENY THE FACT IT'S A FUCKING DIVERGENT SERIES.

That's even the name of the fucking book you can look it up in. G.H.Hardy: Divergent Series.
1) Get it from your library.
2) Realise that a 'real mathematician ... the purest of the pure' does this.
3) Realise you're a cocky-ass undergraduate that thinks because he took a couple of calculus classes that he knows everything.
4) Dismount mount stupid.
5) Shut the fuck up.
7) ???
8) Profit.

>> No.6509564

42

>> No.6509565

>>6509101

Agreed. Can't top that shit.

>> No.6509568

pV = NT

Simple and balanced

>> No.6509583

>>6509568
>not the superior p = nKT

>> No.6509586

I think the fundamental theorem of calculus looks great.

>> No.6509588

>>6509568
i thought it was PV=nRT?

>> No.6509598

dN/dt=r(1-N/K)

>> No.6509607

>>6509588
pv=mRT

>> No.6509610

>e^ipi+1=0
I currently think this equation is garbage; an accident resulting from how we choose to represent our equations. I don't think this would have any meaning or use to some hypothetical alien species that uses a different representation of math (as opposed to something like e=mc^2 which is a universal constant [as far as we know]).

>> No.6509619

>>6509610
Well that's a nice opinion, but if you actually look up how this equation comes about you might change your mind.

>> No.6509632

>>6509619
It comes about because we use "squaring", which is a pretty awkward operation. I didn't work it out completely, but I believe if our mathematical system kept left-multiplication and right-multiplication separate, then instead of having imaginary numbers we would just have two solution cases for the square root of a positive number and two solution cases for the square root of a negative number, both of which would be within the realm of "normally" defined numbers.

You very well could get rid of imaginary numbers if you were absolutely determined to do so, it's just that doing so requires a more complicated system of math.

>> No.6509640

>>6509529
Because it's divergent series, it means you can't just say the sum is equal to some single finite value. Of course you can in some situations use some such value in place of that if that makes sense there, but it doesn't mean the actual sum is equal to that shit.

>> No.6509641

>>6509607
What is this mech E riff raff doing here?

>> No.6509642

>>6509598
I don't know that one. What is it for?

>> No.6509649

>>6509632
nigga u gay

>> No.6509656

>>6509642
I think it's the logistic equation. It's been a while since I've seen it though.

>> No.6509657

1+1=2

everything extends from there

>> No.6509662

>>6509607

not PV=nRT

what the fuck are you doing

>> No.6509663
File: 29 KB, 396x400, But that&#039;s wrong you fucking retard.jpg [View same] [iqdb] [saucenao] [google]
6509663

>>6508999

>> No.6509670

>no entropy
this thread blows

<span class="math">S = k_{B}ln \omega[/spoiler]

>> No.6509673

Faggots, it's dS/dt ≥ 0.

>> No.6509674

>>6509670
My latex skills blow too. supposed to be capital omega

>> No.6509675

>>6509101
Yeah, this shit.

crazy

>> No.6509677

>>6509662
> what the fuck are you doing
Thermodynamics

>> No.6509683
File: 27 KB, 543x335, natural construction.png [View same] [iqdb] [saucenao] [google]
6509683

>>6509657
not really.

>> No.6509686

>yfw humans will never be smart enough to figure out the master equation

>> No.6509691

>>6509640
READ THE FUCKING BOOK.

>> No.6509694

<span class="math">\color{red}{R} + \color{green}{G} + \color{blue}{B}[/spoiler]

Not an equation but it's got beauty.

>> No.6509705

Implying <span class="math">e^{-p}+1=0[/spoiler]

Now <span class="math">e^{i\pi}+1=0[/spoiler] is an equation I can get behind.

>> No.6509706

(ufloat)(double) int x = 5.05;

>> No.6509711 [DELETED] 

<span class="math">\displaystyle \Omega \rho = \int_0^\infty \alpha \gamma2 \omega_t[/spoiler]

newbs

>> No.6509738

>>6509677

right and thermodynamics is PV=nRT you only use the m/M never mRT.

>> No.6509745

>>6509738
what are you on about?
why the fuck would I care about the number of moles?

Mass is much more important

>> No.6509785
File: 1 KB, 244x48, Information Entropy.png [View same] [iqdb] [saucenao] [google]
6509785

>>6509598
I love this equation so much. It is an excellent model for self-replicating phenomena.
>>6509670
That is a good one, but the general form is much better. The picture is related cause I can't remember how to use LaTex.

>> No.6509813

>>6509785
>the general form
no<div class="math">S= \mathrm {tr} ( \hat { \rho} \ln ( \hat { \rho} ))</div>

>> No.6509873

>>6509745

Because it's useful in thermochemistry and is far more important for using it to calculate the stoichiometric relationship between a gas and another substance.

>> No.6509926

>>6509873
> thermochemistry
I thought I smelled a chemist/ChemE.

Only reactions important in my life are
Hydrocarbon + Air -> Energy