/sci/ - Science & Math

You could probably write an interative lambda equation which iterates pi pretty easily. Basically a summation.

http://blog.wolfram.com/2011/06/30/all-rational-approximations-of-pi-are-useless/

How do you do "TeX/jsMath" fractions on this board?

For example, how would I make "6/5" show up as a classical-looking fraction, with 6 on top of a horizontal bar over 5?

>>3466320

This one is accurate to 52 decimal places.

>>3466338
it's easier to just know 52 places of <span class="math">\pi[/spoiler].

i memorized ~ 60 because i was bored. it took like 2 days, and now i can recite them to the tunes of various songs. it's kinda fun, but mostly just for that novelty (and winning prized in <span class="math">\pi[/spoiler] competitions).

>>3466331
Thanks!

@OP – this isn't as accurate as yours, but I discovered π≈<span class="math">\frac{6}{5}[/spoiler]φ².

>>3466370
you could write
<span class="math">\pi \approx \frac{6}{5} \phi ^2[/spoiler]
to make it more legible.

>>3466331

How do you do a cubic or fourth root? That chart just shows how to do square roots.

>>3466386
Yeah. I basically copied everything except the fraction from Microsoft Word. :P

But I'll get a hang of the math tags eventually. How do you do roots other than square roots? The chart doesn't really say.

>>3466390
>>3466398
you'll have to find a list of TeX functions on your own!
i have a pic of most of em, but c'mon you have to do some of the work!

also, calling Josef:
<div class="math">\mathrm{nlog}_k (x) = \int_0^x \left ( \prod_{j=0}^{k-1} \frac {1} {1+ \mathrm{nlog}_j (t) } \right ) \mathrm{d}t</div>

>>3466390
>>3466398

Oh hey, never mind. Found out from Google.

Testing – <span class="math">\tau \approx \sqrt[4]{\frac{17144}{11}}[/spoiler].

>>3466359
Look up the pi song. I think it goes up to 69 or 76 characters.

3.1415926535897932384264338327950288419716939937510582057494459

And that's just the first verse, though I think the second one starts off at like the 120th spot for some retarded reason

>>3466448
Okay, now that I've got this down, here are some approximations I've found, in order of accuracy from least to greatest. Hopefully I didn't make any errors in the coding.

<span class="math">\tau\approx\phi^(\frac{317}{83})[/spoiler]
<span class="math">\tau\approx\sqrt(\frac{904}{97}\phi^3)[/spoiler]
<span class="math">\tau^(\frac{\tau}{3})\approx\phi^8–\phi^{-8}[/spoiler]
<span class="math">\tau\approx2^(\frac{16837}{6350})[/spoiler]
<span class="math">\tau^\tau\approx103541[/spoiler]
<span class="math">\tau\approx\phi^(\frac{20773}{5439})[/spoiler]
<span class="math">\tau^\pi\approx\frac{2896}{9}[/spoiler]
<span class="math">\tau\approx\phi^(\frac{15659}{4100})[/spoiler]

>>3466496
Ugh, let me try that again.

<span class="math">\tau\approx\phi^{(\frac{317}{83})}[/spoiler]
<span class="math">\tau\approx\sqrt{(\frac{904}{97}\phi^3)}[/spoiler]
<span class="math">\tau^{(\frac{\tau}{3})}\approx\phi^8–\phi^{-8}[/spoiler]
<span class="math">\tau\approx2^{(\frac{16837}{6350})}[/spoiler]
<span class="math">\tau^\tau\approx103541[/spoiler]
<span class="math">\tau\approx\phi^{(\frac{20773}{5439})}[/spoiler]
<span class="math">\tau^\pi\approx\frac{2896}{9}[/spoiler]
<span class="math">\tau\approx\phi^{(\frac{15659}{4100})}[/spoiler]

>>3466496
Have you ever considered programming?

You were able to pick up that Latex syntax no shit.

Watch your SICP, get a C/C++ reference, and go at it man.

>>3466496
yeahhh, you'd better read this again >>3466331

>>3466506
That's much better, but a lot of the text is very small. Can that be helped, or is it just an unavoidable consequence of using this format?

>>3466510
use the 'eqn' tags instead of 'math'

<span class="math">\pi > \tau[/spoiler]

>>3466517
Alright. Testing....

<div class="math">\tau\approx\frac{12}{5}\phi^2</div>

>>3466519
I personally prefer Tau for two reasons.

1. It makes more sense, trigonometrically, since the number of radians in one unity of arc is <span class="math">2\pi[/spoiler], rather than <span class="math">\pi[/spoiler].

2. I discovered <span class="math">2\pi[/spoiler] independently, before being taught about <span class="math">\pi[/spoiler] in school, and kept <span class="math">2\pi[/spoiler] saved as a variable to my calculator for many years. (I only recently found out that people sometimes use <span class="math">\tau[/spoiler] to represent <span class="math">2\pi[/spoiler], and I've taken a liking to this usage.)

Who gives a shit about using pi or tau?

More relevantly, is there any real aim to these approximations?

>>3466545
i agree completely.
except i can't get over
<span class="math">e^{i \pi} + 1 = 0[/spoiler]

>>3466564

e^it = 1 so e^it - 1 = 0

>>3466564
<span class="math">e^{2i\pi}-1=0[/spoiler]

>>3466563
>More relevantly, is there any real aim to these approximations?

Prolly not. But it's fun to try and find them in your free time. I have <span class="math">\phi[/spoiler] saved to my calculator as a variable, as well as <span class="math">\tau[/spoiler], so a lot of mine involve them.

Actually, I've got a lot of variables saved to my calculator.

<span class="math">A=\tau\approx6.28319[/spoiler].
<span class="math">B=\phi\approx1.61803[/spoiler].
<span class="math">C=\frac{\tau}{360}\approx0.01745[/spoiler], the number of radians in one degree.
<span class="math">D=\sqrt[12]{2}\approx1.05946[/spoiler], the ratio of two adjacent musical note frequencies to each other.
<span class="math">E=\sqrt[5]{100}\approx2.51189[/spoiler], the base of the logarithmic scale of stellar brightness magnitudes.
<span class="math">F=\frac{6371}{360}\tau\approx111.19493[/spoiler], the number of kilometers per degree of latitude on the surface of the earth.
<span class="math">G\approx6.673848\cdot10^{-11}[/spoiler], the gravitational constant.

>>3466611
"the half step in 12-TET", not "two adjacent musical note frequencies to each other". And don't scientific calculators usually have a lot of these?

>>3466434 nlog, calling Josef
Josef reporting in!

>>3466583
>>3466582
see those are nice, but it's not what i like about <span class="math">e^{i \pi} + 1 = 0[/spoiler].
i like it because it shows that an exponential can give a negative value. at least that's what i loved about it when i first found out about it; that it was so different and unique than any other (non-complex) exponential function.
whereas <span class="math">e^{i \tau} - 1 = 0[/spoiler] looks like it could be any other exponential function.
anyway, it's just an emotional thing about what first got me into loving complex numbers.

in reality i do think we should be using <span class="math">\tau[/spoiler]

>>3466649

Looks like you destroyed taufags last standing place

>>3466634
>"the half step in 12-TET", not "two adjacent musical note frequencies to each other".

*shrug*
If you want to get technical.

>And don't scientific calculators usually have a lot of these?

I'm actually using a regular old TI-85 graphing calculator. My mom used it in college, and left it here after she moved out.

>>3466638
oh perfect!
so have you made any progress on the nlog?

i haven't been able to stop thinking about it, and i can't see a way to expand the index to <span class="math">\mathbb{R}^+[/spoiler]. i think i can show that it can't be done, but i need some help on the math.

>>3466663 so have you made any progress on the nlog?
I'm afraid not, I didn't get any new ideas and lost track of it. I found a paper on finding the root of <span class="math">\exp[/spoiler], but it wasn't very easy to understand and my studies kept taking more and more time. I don't think this is going to become any better in the next weeks. :|

I don't want to use any more than eight variables on my calculator, because I like using I and J as free variables for my momentary calculating needs. So I'm really trying to put a lot of thought into what I should use variable H for.

I'm thinking I should make it <span class="math">H=299792.458[/spoiler], the number of kilometers traveled in a vacuum by light in one second; but since I already know by heart the length of one astronomical unit (149598261 kilometers) and the amount of time it takes for sunlight to reach the earth (499.00609 seconds), it seems to me that this would be superfluous. I'm thinking instead of saving the length of one parsec (206264.806 astronomical units, or 1191.289 light-days), though I can't decide on a unit. I dunno. I'll have to think more on it.

>>3466611
>Prolly not. But it's fun to try and find them in your free time.

Bleh. Why not do something less trod on? You like compact representations of data; try learning Huffman coding.

>>3466711 try learning Huffman coding
Screw Huffman, I've got a more compact way. Pic related, correct to more than 100 digits.

>>3466728
I meant, as a sort of starting point for learning information theory.

>>3466746
Thanks for clarifying that.

>>3466728
>Pic related, correct to more than 100 digits.

:/
Yeah, but it's so huge as to be mnemonicly useless.

I prefer the approximations that aren't just rational fractions. Like OP's <span class="math">\sqrt[4]{\frac{17144}{11}}[/spoiler]. It's not accurate to nearly as many digits, but at least it's kind of memorable.

Now, if you could find an approximation to a hundred digits that was something as simple as that, that would be something different.

>>3466752
wär's dir lieber ich wär ein ungeduschter Amerikaner mit Harry Potter Brille und verfilztem Haar? ^^
Oder wie ist "Betrug" gemeint?

>>3466769 Yeah, but it's so huge
Wat? <span class="math">\mathrm{Rationalize}[\pi,10^{-100}][/spoiler] is huge?

>>3466770
Aber hallo! Ich werde dir zu ehren drei Tage nicht duschen und dir dann ein Foto von mir schicken. (Okay, lieber doch nicht)

pi = 4*arctan(1)

>>3466769
>Yeah, but it's so huge

That's what she said.

>>3466780
Captain Obvious is online.

>>3466779
In wahrheit war der Typ im Video nur ein stunt-double und ich bin eigentlich Emma Stone - alles was du hier ließt hab ich zuerst duch nen online-translater gejagt. Ich hoffe jetzt wo du die Wahrheit weißt fühlst du dich nichtmehr betrogen.

So, has anyone else noticed this?

<div class="math">\tau^{\tau}\approx\phi^{24}</div>
<div class="math">\tau^{\frac{\tau}{2}}\approx\phi^{12}</div>
<div class="math">\tau^{\frac{\tau}{3}}\approx\phi^{8}</div>
<div class="math">\tau^{\frac{\tau}{4}}\approx\phi^{6}</div>
<div class="math">\tau^{\frac{\tau}{6}}\approx\phi^{4}</div>
<div class="math">\tau^{\frac{\tau}{8}}\approx\phi^{3}</div>
<div class="math">\tau^{\frac{\tau}{12}}\approx\phi^{2}</div>
<div class="math">\tau^{\frac{\tau}{24}}\approx\phi</div>

>>3466793
Meine Menschenkenntnis sagt mir, dass du eventuell flunkerst, aber was hab ich zu verlieren ... Date? ;-)

Tragt eure Schwulitäten nicht in diesem Thread aus.

>>3466812 Thread
Was ist das denn für ein Zangendeutsch? Derartige Gossensprache wird hier nicht geduldet!

>>3466805
Sure. I like me some german nerds.

>>3466804
That's just power rules man. One of those is the same as the rest.

>>3466816
I'm not a nerd, it's perfectly normal to read books on gauge field theory when coming home drunk at 5 am in the morning!

>>3466822
was ist eigentlich deine Ansicht zur Korrespondenz zwischen physikalischer Theorie und Realtität?

>>3466836
Disjunkt, aber man muss sich immer wieder dran erinnern, sonst glaubt man man irgendwann die Welt bestehe aus Physik.

>>3466839
>Welt bestehe aus Physik.

>implying it doesn't

Atheists 1
Christians 0

>>3466819
>That's just power rules man. One of those is the same as the rest.

I'm aware of that, but check out how accurate the ones in the middle are.

Also, there's this one.
<div class="math">\tau^{\frac{\tau}{3}}\approx\phi^{8}–\phi^{-8}</div>

>>3466819
>That's just power rules man. One of those is the same as the rest.

I'm aware of that, but check out how accurate the ones in the middle are.

Also, there's this one.
<div class="math">\tau^{\frac{tau}{3}}\approx\phi^{8}–\phi^{-8}</div>

>>3466839
"gibt es zu viele disjunkte Pfade musst du dir die Frage stellen was Wahr ist"

:)

>>3466804
<span class="math">\phi^{24}[/spoiler] NONRENORMALIZABLEinfourdimensions
<span class="math">\phi^{12}[/spoiler] NONRENORMALIZABLEinfourdimensions
<span class="math">\phi^{8}[/spoiler] NONRENORMALIZABLEinfourdimensions
<span class="math">\phi^{6}[/spoiler] NONRENORMALIZABLEinfourdimensions
<span class="math">\phi^{4}[/spoiler] RENORMALIZABLEinfourdimensions
<span class="math">\phi^{3}[/spoiler] SUPERRENORMALIZABLEinfourdimensions
<span class="math">\phi^{2}[/spoiler] BORINGinalldimensions
<span class="math">\phi^{1}[/spoiler] WTFinalldimensions

>>3466871
Es ärgert mich jedes mal persönlich wenn jemand mir erzählen will, dass da wirklich Elektronen durch irgendwas fliegen.

this is the simplest I can remember, 113355, then written as 355/113, exact to 6 digits, 7th digit is 9 instead of 6, so it's pretty accurate for the simple form. Discovered by some Chinese mathematician, some thousands years ago.

>>3466902
It's called Milü, and he was an astronomer. (anon, for all your pointless historical needs)

>>3466883
aha, dann bist du doch schon sehr am Trennen der beiden. Das find ich gut, das ist eine gute Gesprächsbasis.

PS: Weißt du was bei phi^1 passiert? Ich würde raten, dass da einfach alle lösungen mit der Zeit explodieren, i.e. die Greenfunktionen werden immer größer auch wenn nix passiert.

>>3466943
>dann bist du doch schon sehr am Trennen der beiden
Ich trenne die beiden nicht sehr, ich trenne sie. Das war die wertvollste Erkenntnis, die ich in meinen Nebenfach-Philosophie-Exkursionen gelernt habe. Vorher war ich der beschränkte Standardphysiker. Ja, ist mir peinlich.
>Weißt du was bei phi^1
Öh, nein. Wobei, wenn man 1PI-Diagramme konstruiert erfindet man ja auch einfach so ne Wechselwirkung <span class="math">\int\mathrm dx\varphi(x)\int\mathrm dy\varphi(y)[/spoiler] die einem die Graphen zerschneidet. Lässt man jetzt eins der Integrale weg machts halt einfach plop und das Teilchen ist weg. Da hat die Impulserhaltung sicher was dagegen.

damn, german people know their science very well

>>3466920

oh, my bad, astronomer and mathematician, and it wasn't thousands of year before, only about 1600 years. But you've got to admit, it's simple and pretty accurate for what it was.

http://en.wikipedia.org/wiki/Zu_Chongzhi

>>3466780
arccos(-1)

>>3466987
Certainly. Chinese maths was badass.

Not as badass as Indians writing it in fucking verse, though. U mad TeX?

>>3466966
Josef, is it bad that i really dislike your notation <span class="math">\int dx f(x)[/spoiler] as opposed to <span class="math">\int f(x) dx[/spoiler]

>>3467015
Only homosexuals are allowed to use this notation.

>>3467015
Writing the <span class="math">\mathrm dx[/spoiler] at the end of the integral really isn't an option in physics when the integrals are long, nested and what not.
Apart from that, you don't write something like <span class="math">\mathrm d(f(x) + akhflksjhflk) / \mathrm dx[/spoiler] for the derivative for the same reason. The integral is just a linear operator after all, and I like my operators on the left.

>>3466966
hehe, ja ich hab auch einiges Gelertn in der philo Vorlesung die wir hatten. Mittlerweile interessiere ich mich ziemlich für Wissenschaftstheorie

>>3467031
But you have to use a lot of parentheses this way.
<span class="math">\int dx f(x) + a \neq (\int dx f(x)) + a[/spoiler]

>>3467038
You don't write parentheses around <span class="math">\sum_nf(n)+a[/spoiler] as well. Summation ends the integral, that's it.

>>3467044
Anyway you have to put more expressions in parentheses like <span class="math">\int dx (f(x) + a)[/spoiler] instead of <span class="math">\int f(x) + a\ dx[/spoiler]

>>3467060
I've been using them for quite a long time now, and
a) Notation isn't about being short in terms of not generating parentheses, it's about convenience. Searching a 3 line integrand for the differential is not a fun thing to do. Example:<div class="math">Z=\prod_{k_<}\int\mathrm ds_{k_<}\exp\left(hs_0-\frac12\int_{k_<}k_<^2s_{k_<}s_{-k_<}-\omega\int_{k_<k'_&lt
;}^{|k+k'|<b^{-1}\Lambda}s_{k_<}s_{k'_<}s_{-k_<-k'_<}\prod_{k_>}\int\mathrm ds_{k_>}\exp\left(-\frac12\int_{k_>}k_>^2s_{k_>}s_{-k_>}\right)\exp\left(-2\omega\int
_{k'_<}s_{k'_<}\int_{k_>}s_{k_>}s_{-k_>-k'_<}-\omega\int_{k_>k'_<}s_{k_>}
s_{k'_>}s_{-k_>-k'_>}\right)\right)</div>
(This one also leaves away some differentials altogether.)
b) Sums don't occur that often, and even if - every exp() requires parentheses as well, actually - every function does (if it's not a short one like sin x, arguably)

>>3467095
Well, to each his own.
Btw, what's the meaning of this horrifying LaTeX expression in physics?

>>3467095
Holy fucking Moses, Josef.

So is that entire expression inside the argument of the first product?
And, everything to the right of the second product is in it's argument?

<div class="math">\pi = \frac{\log 262537412640768744}{\sqrt{163}}</div>

>>3467095

>integral within an integral

we need to go deeper.

oh man, i can't wait to see this with math tags
<span class="math">Z=\prod_{k_<}\int\mathrm ds_{k_<}\exp\left(hs_0-\frac12\int_{k_<}k_<^2s_{k_<}s_{-k_<}-\omega\int_{k_<k'_&lt
; ;}^{|k+k'|<b^{-1}\Lambda}s_{k_<}s_{k'_<}s_{-k_<-k'_<}\prod_{k_>}\int\mathrm ds_{k_>}\exp\left(-\frac12\int_{k_>}k_>^2s_{k_>}s_{-k_>}\right)\exp\left(-2\omega\int _{k'_<}s_{k'_<}\int_{k_>}s_{k_>}s_{-k_>-k'_<}-\omega\int_{k_>k'_<}s_{k_>} s_{k'_>}s_{-k_>-k'_>}\right)\right)[/spoiler]

>>3467143

>>3467117
It's the partition function of a (simple) spin system getting ready for renormalization (note the cut-off-y parameter <span class="math">\Lambda[/spoiler]) (Inb4 cutoff sucks. It's not cutoff.). It's not that complicated if you've seen where it comes from and understand where it's supposed to lead you.

Fun (read: asshole) exercise to learn inventing and using new notation on the fly: Prove the Jacobi identity on the pic.

More fugly formulas! Pic's the time-sliced path integral for the free quantum-mechanical particle. Again, lots of integrals, and lots of differentials right after them. (Infinitely many, actually.)

>>3467154
lolz.
How long is the proof?
Doesn't seem very difficult, but looks like a shitload of wasting time.

>>3467180
Now you're trolling.
>implying anyone on /sci/ is gonna understand this expression.

>>3467154
Fascinating... I'm sure I'll like it once I can remotely understand what that is.

Also
>>3467095
>This one also leaves away some differentials altogether
Is this typical? Because I hate when people/authors do this.
Is it just because it's supposed to be obvious at this level, and that would just kinda waste space/time/energy?

>>3467189 How long is the proof?
Depends on how compact your notation is. Writing out all the differential quotients I'd estimate a few pages, I've done it in one, and writing small and leaving out steps maybe one half.

Pic's an index battle. Normally, indices are simply left away in this case. (I could go on posting stuff like that for days, I should make a math gore thread or something)

>>3467205 I should make a math gore thread or something
Fucking lol'd. This should definitely happen.

>>3467200
>I'm sure I'll like it once I can remotely understand what that is.
No. It's not particularly awesome. (And the proof really sucks ass. I've got it handwritten here, it's a massive amount of symbols that loooove to be mixed up when you're doing the problem.)
On the other hand, Lie groups/algebras in general are kind of nice.
>Is this typical?
In some parts of physics yes, but usually no confusion can arise. For example, prior to the Z formula given above, it was stated that <span class="math">\int_k\equiv \int_{\mathbb R^D}\mathrm d^Dk[/spoiler]. Spins (<span class="math">s_k[/spoiler] etc) remain in the usual notation.

>>3467218
I'd start one if I didn't have to get up early tomorrow. Meh

>>3467200
Oh, I actually made it in half a page, some steps are on the first page, and when it's fully blown up terms start canceling. Pic related. The image quality is appropriate for the fun I had doing this.

>>3467224 <span class="math">\int_k\equiv \int_{\mathbb R^D}\mathrm d^Dk[/spoiler]
So what would the "correct" (with all the differentials and correct notation) equation look like for this one?

Bumping with the commutator of angular momentum operators, 2nd QFT problem sheet, man all the exercises were like that

>>3467282
<span class="math">\int_{\mathbb R^D}\mathrm d^Dk[/spoiler] is the correct notation. It's the integral over the whole D-dimensional space. The short notation for it is <span class="math">\int_k[/spoiler] in the case above.

>>3467313
You should post some of these pictures anonymously and pretend to need help with your homework.

This thread reminds me that I've got to finish to write the Einstein equations on a single sheet of paper - in broken-down-to-g form. Pic's the first 4 lines, together with the huge badbox that is yet to be replaced by many newlines.

>>3467282
>>3467313
however, both sides of the equation are shortcuts for something.

int d^3x f(x,y,z) is

limit of sum of ... (limit of sum of ... (limit of sum of ... f(x,y,z)))

>>3467330
Hey guys, I'm new to this board and I was wondering how to solve this:

Let
- <span class="math">X_1,X_2\in\mathcal X(M)[/spoiler], <span class="math">Y_1,Y_2\in\mathcal X(N)[/spoiler] (<span class="math">\mathcal X[/spoiler]: smooth vector fields; <span class="math">M,N[/spoiler]: smooth manifolds)
- <span class="math">F\;:~M\rightarrow N[/spoiler] be a smooth map
- <span class="math">[\cdot,\cdot][/spoiler] be the vector field commutator, defined by <span class="math">[X,Y]=\sum_j\left(X(\eta^i)-Y(\xi^i)\right)\frac{\partial}{\partial x^i}[/spoiler], where <span class="math">\xi,\eta[/spoiler] are the components of <span class="math">X,Y[/spoiler] respectively.

If <span class="math">Y_j(F(x))=\mathrm dF_x(X_j(x))[/spoiler] (<span class="math">j=1,2[/spoiler]), show that<div class="math">\mathrm dF_x([X_1,X_2](x))=[Y_1,Y_2](F(x))</div>

>>3467330
lol, then complain when /sci/ can't do them

> Mathematical Physics
> Nope, certainly not beautiful.

nope.jpg

>>3467348 limit of sum of
Don't be silly ;-)

>>3467362
Fucking lol'd so hard.

>>3467369
Those equations were all normal theoretical physics, nothing mathematical about them. >>3467362 posted a math problem which isn't physics though.

Ever wondered how the beautiful orbitals of the hydrogen atom look like as an equation?

>>3467342
>2011
>not using mathematica for nasty shit like this
>Emma Stone will not date you

>>3467386
Thanks for making me look up what a smooth manifold is.
In which semester did you learn this?

>>3467406 In which semester did you learn this?
"Officially" in a course, never. Stumbled upon it more or less by myself around the 5th.

>>3467405
I used a PHP script to generate the LaTeX. The problem with Mathematica is that it's awful to handle strings with it compared to PHP.
Anyway, is that a custom script or some tensor package?

Maxwell's equations in not-so-beautiful notation (and flat 3D space etc)

>>3467400
>mfw we actually kinda did this in my last physics class so I roughly know what you're talking about.

Also
>2011
>using \vartheta
i hope you don't do this

>>3467421
Nur ein Weilchen später $\ |\ $ schrieb man sie kompakt an $\ |\ $ mit Vektoren!\\

>>3467431
\theta can kiss my ass! Burn you ugly fuck! <span class="math">\not\theta\!\!\!\backslash[/spoiler]
<span class="math">\varepsilon\varphi\vartheta[/spoiler]

>>3467430
Hättest du den Text wohl irgendwo in Textform und würdest ihn mir gerne rüberwedgen?

>>3467454
naaa, solche Texte sind zu jedem Zeitpunkt unkomplett und work in progress.
Aber du kannst ja das video gern weiterleiten, ich freu mich ja auch über view ;)

>>3467439
<span class="math">\theta \gg \vartheta[/spoiler]
<span class="math">\phi > \varphi[/spoiler]
<span class="math">\epsilon \approx \varepsilon \mathrm{ depending on the situation.}[/spoiler]

>>3467505
You're an evil person. (Actually it's often useful to have two different thetas and phis, but I prefer the var versions.)

Speaking of usefulness: I need some sleep, 12 hour day ahead. Good night.

>>3467518
>You're an evil person.
<span class="math">\ddot{\smile}[/spoiler]

>Actually it's often useful to have two different thetas and phis, but I prefer the var versions.
Yeah, that's true. Yay for opinions (although your opinion is objectively incorrect)!

>Speaking of usefulness: I need some sleep, 12 hour day ahead. Good night.
Goodnight!

>mfw I'm going into my 3rd year of pure maths this fall and I have no idea what the fuck is going on in this thread

>>3467586
Now this is fail.
I'm gonna start my first year in math soon and I understood most of this shit.

>>3467591
Grad or undergrad?

Because I truly commend you if you can follow this out of high school.

>>3467618
Thanks.
As a eurofag I dunno what "grad" or "undergrad" means.

>>3467625
Ah, okay.
How long have you been in university?
or, How old are you?

>>3467639

I'm 20 and will start university this autumn.

>>3467646
Wow, good for you.
Did you study this math in school, or did you do it independently?

>>3467684
I read some books just for interest. And whenever I came across anything on /sci/ which I didn't understand, I looked it up.

>>3467705
Cool, good luck in the future man! You sound like a smart guy.

>>3467727
Thanks dude. Have a nice day.

>>3466281
Has anyone done a nifty plot of the successive fractional approximations of pie on an x/y chart?

>>3467773
you mean like the one in the link on the third post of this thread?

355/113

>I'm gonna start my first year in math soon and I understood most of this shit.
Sure. Care to explain how to calculate <span class="math">\int_{\mathbb R^D}\mathrm d^Dk[/spoiler]? What a smooth vector field on a manifold is? What <span class="math">\theta^i{}_j[/spoiler] stands for?