/sci/ - Science & Math

>>7005703
Reddit pls go.

2+ 3 = 5

Barnett's Identity

p*e = n*i*s

>>7005703
>unironically being in high school

>>7005703
>being this reddit
Nature is incredible

Math is not "beautiful". It's perfect. All of it. There is no beautiful equation. It's all uninteresting, completely justifiable logic. It's absolutely perfect and your romance you bring to it is fucking autistic
>inb4 autism
No your a autistic :^)

>>7005736
>muh logic-emotion dichotomy
So plebeian. The sign of a plebeian who is deficient both in logic and in emotion.

Beauty is a concept made of the logical architecture of your neural system. Determination of beauty is a higher algorithm and it is perfectly valid to take the concepts of logic as inputs and they often have a high output.

>>7005751
>implying Lenardo had emotions

>>7005727
Nice contribution.

>>7005703
pic related

principle of least action
if you disagree you're a pleb

>>7005882
tfw feynmann was so obsessed with it he re-formed quantum using it
really is sexy
especially when you study why classical particles follow classical path

>>7006030
why?
All I got was Feynman's hand-wavy explanation

>>7006033
why to which

>>7005871
Why not take the reciprocal of both sides... would be cleaner

1=0.999999.....

best

>>7006042
<span class="math">\frac{1}{\phi} = 1 + \phi[/spoiler]

>>7005703
anyone else enjoy asymptotics?

<span class="math"> n!\sim n^{n-\frac{1}{2}}e^{-n}\sqrt{2 \pi} \; \; n\rightarrow \infty [/spoiler]

>>7006042
you can't even get the equation right
>reddit high schooler detected

>>7006042
>>7006048
>>7006063
what's so great about this?

>>7006035
why do classical particles follow the classical path?

>>7006057
idiot

>>7006069
Nothing really. But it's solution has an interesting continued fraction:
<span class="math">\phi = 1+\frac{1}{1+\frac{1}{1+\frac{1}{1+...}}}[/spoiler]
Proof is super straight-forward.

>>7005703
<span class="math"> W=\int_{k<\Lambda}[Dg][DA][D\psi][D\Phi]exp \left \{ i\int d^4x \sqrt{-g} \left [ \frac{m^2 _p}{2}R-\frac{1}{4}F^a _{\mu \nu}F^{a \mu \nu}+i \bar{\psi}\gamma ^{\mu}D_{\mu}\psi ^{i}+\left ( \bar{\psi}^i _L V_{ij}\Phi \psi ^j _R +h.c. \right ) -|D_{\mu}\Phi |^2 -V(\Phi) \right ] \right \} [/spoiler]

Everyone else can back the fuck up

^
|
|
what the fuck?

>>7006089
Can anyone give a play by play explanation for this one??

>>7006089
that is some beautiful shit right there

>>7006089
Path integral?

>>7006089
dat sum quantization functional sheit white boy?

>>7006179
Are you asking if this is a functional integral (aka Feynman Path Integral)?
The answer is yes.

>>7006177
Yeeeeeup

i+1=0

le ebin -1/12

>>7005703
PV = nRT

|i|-1=0

I just cannot believe how the length of an imaginary unit is exactly 1.

Mindblowing

>>7008307
lol

>>7008025
this is true for very small values of 1

Cantor diagnolisation is probally my favorite

>>7008290
>not p = nkT

I think quadratics are beautiful. They are so practical, make lovely shapes, and the quadratic formula is just so damn good.

fuck with me I don't give a shit

>>7008641

>>7005751
No your a plebian :^)

Phi / 1 = Phi + 1
1/phi = Phi - 1

(1/phi) *360 = golden angle in degrees

>>7005720

best so far

8=D
("Your Actual Penis Size Equation")

>>7005720
i have an alternative:
3 + 4 = 5

1 + 1 + 2 + 3 + 5 ...

It's called the Fibonacci sequence, it's one of the most important discoveries ever, it explains literally everything about the universe.

>>7005703

What Math level am I suppose to understand this equation?

>>7010136
what does that sum up 2

>writing it like a pleb

>>7010141
You can see 1 + 1 + 2 + 3 + 5 +... is an alternative way of writing 1 + 2 + 3 + 4 + 5 +...., so by the law of contrapositive induction, it is -1/12.

>>7010136

I thought pi did that.

>>7010148
top pleb

>>7006089
This is what theoretical phycisists believe

>>7006079
aka The Golden Ratio
It's all over art and architecture as it's regarded as aesthetically pleasing

>>7010136
It's a sequence not a sum
Should be 1,1,2,3,5,8,...
>>7006048
Also relates to phi as
(n+1)th Fibonacci / nth Fibonacci --> Phi

<span class="math"> k_{\infty} = \eta f p \varepsilon [/spoiler]

>>7010154
>I don't understand the equation
>U-UM THEORETICAL PHYSICISTS BELEIVE THIS LOL!!!!!!?????

>>7005703
-1/12

>>7005703
1 + 69 = 420

poynting vector in lienard-weichert field

>>7006036
The expression would be more complex. Summing the reciprocals would not give you the same answer ie (2+4+8)^-1 does not equal (1/2)+(1/4)+(1/8)

E=MC^2

Simple I know, but that's the beauty of it. With it, we can calculate the total energy of a given object.

>>7010143
That form is more beautiful anyways because its meaning as a 180 degree rotation is manifest when writing it like that.

The summation of every single number is not infinity, but -1/12!

>>7005703
OP learned that the approximate speed of light is always equal to three, and that's why OP loves:

~C=3

>>7006089

>>7006165
the equation that describes everything, gravity aside

>>7010508
>not retarded

okay

>>7006075
Because correspondence principle.

Someone post Barnett's triple integral identity.
Mechanical energy in isolated systems is constant

>>7011458

Barnett integrable functions:
<span class="math">\mathbb{B}={f(x) |\int \int \int f(x) d^3x < \frac{e^{\pi i}}{11.999...}}[/spoiler]

>>7006063
That equation is absolutely correct though... if you reciprocate both side, and substitute ad infinitum, the resulting continued fraction is precisely the golden ratio. He just gave the reciprocity rule for phi.

>>7008552
tip top kek m8

>>7010075
>not using radians
ew
>tfw captcha is diraq

>>7010139
Probably just the series expansion of the exponentiation function, as well as knowledge of limits. Maybe second-year analysis?

>>7010291
I'm so glad this is dying.

>>7010806
>every single number
>what is formality?

>>7011530

>>7011533
lel

>>7006042

lol no

1/4 = 1 + 4

>>7011547
thats not a variable, its a constant like e

>>7011547
it's not
<div class="math"> \forall \phi \in \mathbb{R}: \frac{1}{\phi } = 1 + \phi </div>
it's
<div class="math"> \exists \phi in \mathbb{R}: \frac{1}{\phi} = 1 + \phi </div>

9+10=21

>>7005703
1=0
It's the most beautiful equation because it has no solution and contains the additive and multiplicative identity.

>>7011808
it's not an equation is a false equivalency you faggot

>>7005703
Neutron transport equation. Not gonna type it out though, just google it. Or go here: http://en.wikipedia.org/wiki/Neutron_transport#Neutron_Transport_Equation

>>7011865
only real answer ITT.

>>7011865
I didn't know that one, but I work with the Boltzmann equation in my physics PhD.
What do you like about that neuron transport equation?

>>7005725
explain yourself

>>7011747
tfw taking lin alg this semester and can understand this
yeah its basic as fucc

Shit like this is cool. Physical models.

1-1+1-1+1...=0.5

>>7011547
its a number with the property that 1/x = 1 + x

multiplying x on both sides, x + x^2 -1 = 0

the solution of x satisifies 1/x = 1 + x

x = golden ratio aka phi

>>7012833
x = golden ratio - 1

i'm sorry. its not yet the golden ratio.

>>7012861
Seconded.

F=dp/dt

Sqrt(2)/2 = 1/Sqrt(2)
>still blows my mind, i literally didn't understand it until this very moment

>>7006089

>not just posting the picture

>>7014158
what's W?

<div class="math">\int_S K dA=2\pi\chi (S)</div>

I like this one

>>7014157
I remember this one taking me sooooo long to get my sophomore year of college. Had no idea why the computer said 1/sqrt(2) when my answer was sqrt(2)/2

>>7014164
Lambert's W function

<span class="math">\delta s=0[\math][/spoiler]

>>7014345
Idiot

<span class="math"> \delta s=0 [/spoiler]

>>7014164
W is the entire thing on the rhs.

<span class="math">\int_\Omega\nabla\times\vec{F}\cdot d\Omega=[/spoiler]<span class="math">\int_{\partial\Omega}\vec{F}\cdot ds[/spoiler]

>>7014735
or better,
<div class="math">\int_{\partial\Omega}\omega=\int_{\Omega}d\omega</div>

Hate to bump this shitty thread but I find cantor's diagonal argument for the uncountability of the reals to be particularly elegant.

in b4 wildassberger

I wouldn't say its my favourite. But its up there.
>>7014735
>>7014755

>>7015289
>equation

>>7014367
go to bed Joseph-Louis

You should be able to prove this.

>>7015807
Glad to see the residue theorem here

>>7015289
That's not an equation.

>>7015807
Go away!
I wasted months with this shit.

>>7010672
Bro do you even special relativity ?

E = sqrt ( (mc^2)^2 + (pc)^2 )

You gave the formula for the rest mass...

>>7008290
How about
E = 3/2 KT ?
One (e.g. me) can proof that that is true for a much broader array of gasses. Even for bose einstein condensated or Fermi dirac gasses

>>7015788
not wasting my time on easy shit anon.

No contest

>>7015904
But.. ;-;

>>7016606
>equations
>posts inequality
Go suck some cock.

>>7016606
>not the generalized form
Gross

>>7016615
>>including the imaginary part
>>pls go

>>7016373
I would hope you'd be able to, otherwise you might want to just give up the whole STEM thing.

>>7016624
pic related, then just put energy (1/2mv^2) into the boltzmann distribution function and find the volume average. <1/2mv^2> = 3/2kT for 3 dimensional case.

>>7014755
This. Also
<span class="math">\dot q = \frac{\partial H}{\partial p}[/spoiler]
<span class="math">\dot p = -\frac{\partial H}{\partial q}[/spoiler]

>>7010148
pi * fibonacci * phi = elon musks IQ in sexagesimal

>>7010136
You're fucking retarded

>>7014164
The state sum amplitude

Gaussian Function. Bell curves are by far my favorite shape made by a single line. They're so damn symmetrical AND are in basically every cycle.

>>7010146
that still bothers me

The Taylor series stuff is pretty cool

>>7006057
Nice formula but why did you divide by n on the right side? Now it's incorrect.

>>7006057
Stirling's approximation. Really nice.

a^2 + b^2 = c^2

>PhD in Functional Integration
>600k per year
>step up triple integral fags.

P = NP

>>7018479
how? I am a pure math phd and barely manage $300k per year with whatever job I want

also, how do you setup triple integrals?

d^2 = 0

>>7017308
Pretty sure it's the correct representation

>>7018507
?
Take calculus

Currently studying the beauty (and complexity) of quantum mechanics. Here is Schrodinger's time-independent equation... [-ℏ^2/2m∂^2/(∂x)^2 + PE]ψ=[iℏ∂/∂t]ψ

>>7018517
>claims triple integrals are easy after undergrad calculus

oh wow

ayy lmao

<span class="math">i \hbar \gamma^{\mu} \partial_{\mu} \psi - mc \psi = 0[/spoiler]

Lol hurr durr newton second law E=ma
>OP an hero

>No based Ohm's Law

posting in ebin reddit thread

>>7018517
>areyoufuckingkiddingme.300k

>>7018544
>not setting <span class="math">\hbar=c=1[/spoiler]
>not writing <span class="math">\gamma^\mu\partial_\mu =: \not\partial[/spoiler]

>>7016636
He didn't actually want you to do it.

>>7010146
The toppest of keks.

>>7010139
https://www.khanacademy.org/math/integral-calculus/sequences_series_approx_calc/maclaurin_taylor/v/euler-s-formula-and-euler-s-identity

>>7011865
>I like long, overly complicated equations because I can show off how smart I am with them

>>7018893
>Projection

Transport theory is actually pretty fun.

>>7018893
>overly complicated
not that guy, but it's literally simple as fuck
>neutrons gained = neutrons lost
ez

>>7014755
Was going to post this.

>>7018898
>I can't into comprehension

Visually, not conceptually complicated, you dolt.

>>7018854
I do what I want

>>7005871
based ramunujan

>>7018903
That transport equation really doesn't fall into any definition I can think of for beauty. The fact that an equation describes something shouldn't make it particularly beautiful, since that is what an equation is supposed to do in the first place. The beauty comes from its uniqueness, cleverness and brevity. So >>7006089
is not very beautiful, it is a list of interactions. On the other hand, Feynman diagrams that succinctly describe all of those interactions are beautiful. Likewise, the beauty of the Dirac equation >>7018544 isn't in the equation itself, but in guessing the wavefunction is a spinor. Ladder operators (another Dirac invention) would also qualify as an example of mathematical beauty.

>>7005703
>integrals

the motherfucking riemann-zeta function just destroys my mind
-1/12 my ass

>>7005723
ebik sci meme :)

>>7016623
>modulus sign
>imaginary part
u wot m8?

>>7018826
>not using guage covariant derivative <span class="math">D_{\mu} = \partial_{\mu} +ieA_{\mu}[/spoiler]

>>7014755
>>7014735

whats these 2

x=(-b±sqrt(b^2-4ac))/2a

>>7021478
Then you'd have to add <span class="math">\frac{1}{4}F_{\mu\nu}F^{\mu\nu}[/spoiler] to make sense. It's just the special case for the QED lagrangian.

>>7005871
I think this is one of Ramanujan's discovery to calcuculate pi fast. it's amazing.

<span class="math">e^{i\frac{\tau}{2}}=-\frac{1}{12}[/spoiler]

>>7021500
Stokes' Theorem
Curl Theorem (which is just Stokes' theorem).

>>7010139
I covered it in my second week of complex analysis, but you would probably see it before then.

>>7016606
>>7016615
See I'm math guy and I never did quantum physics but is the uncertainty principle just a specific form of this result in Functional Analysis.
If so in quantum physics do you just model momentum/position as linear operators on R^3?

>>7018526
They are. They're first year shit?

>>7023125
The momentum operator is just differentiation, which becomes self-adjoint when you restrict the domain sufficiently.

>>7010139
I got this 6 weeks into my first calcuclus class

new on /sci/, can someone explain how you enter mathematical symbols here?
do you add an \ in front of your symbol like you sometimes do?
\pi

>>7023169
Read the sticky

>>7018514
No, it says -1/2; should be +1/2.
The formula becomes correct if you replace the left hand side with Γ(n), which is (n-1)!

>>7023087
>using <span class="math">m_0[/spoiler] for rest mass like there is any other mass than rest mass.
Plus it's not really beautiful. The beautiful part of special relativity is the derivation of the Lorentz/Poincaré group from very simple assumptions.