/sci/ - Science & Math

The length of the curve of <span class="math">y=c\sin(x/a)[/spoiler] over a period is the integral over a period of <span class="math"> \sqrt{
\mathrm{d}x^2 + \mathrm{d}y^2} = \left( \sqrt{1^2+(\mathrm{d}y/
\mathrm{d}x)^2} \right) \mathrm{d}x[/spoiler], so it's
<div class="math">L= \int_{0}^{2\pi a} \sqrt{1+ (c/a)^2\cos^2 (x/a)} \mathrm{d}x = \int_{0}^{2\pi a} \sqrt{1+ (c/a)^2\cos^2 (x/a)} \mathrm{d}x = a\int_{0}^{2\pi} \sqrt{1+ (c/a)^2\cos^2 (u)} \mathrm{d}u</div>
(with <span class="math">u=x/a[/spoiler] and <span class="math">\mathrm{d}x = a\mathrm{d}u[/spoiler])

On the other hand, the perimeter of the ellipse, approached with the same method, is
<div class="math">P= \int_{\theta=0 }^{2\pi} \sqrt{\mathrm{d}x^2+ \mathrm{d}y^2}=\int_0^{2\pi} \sqrt{ a^2\sin^2(\theta) + b^2\cos^2(\theta)}\mathrm{d} \theta =\int_0^{2\pi} \sqrt{ a^2 \left(\sin^2(\theta) + \cos^2(\theta) \right) + (b^2-a^2)\cos^2(\theta)}\mathrm{d} \theta </div> <div class="math">=\int_0^{2\pi} \sqrt{ a^2 + (b^2-a^2)\cos^2(\theta)}\mathrm{d} \theta =a \int_0^{2\pi} \sqrt{1 + ((b/a)^2-1)\cos^2(\theta)}\mathrm{d} \theta</div>

So <span class="math">(b/a)^2-1=(c/a)^2[/spoiler] gives <span class="math">L=P[/spoiler]. I don't know if <span class="math">L=P[/spoiler] is enough or if there is another condition so that a part of the ellipse doesn't "cross" the curve of the sine. I don't know if there are other ways for the two integrals to be equal (well, I don't think so, but I don't know how to prove it). Also, I suck at manipulating integrals, so I'm likely to have done a mistake or two on the way: hopefully the method is still correct.

>>4414610
Also the condition I end up with is <span class="math">b^2=a^2+c^2[/spoiler]. Cooler in this form.

>>4414610
>>4414628
First result on google.
You are disqualified, tripfag shitposter.

>>4414630
Wait... because this is a relatively simple Putnam problem which HAS to be attacked from this angle (since neither the perimeter of an ellipse nor the length of the curve of the sine can be simplified properly, and the question is to make them equal), it means that whoever finds the solution googled it? I am pretty sure no one will come up with a solution that doesn't involve writing the two lengths as integrals and matching them without actually computing them.

...when I post my reasoning bit by bit while thinking, I'm spamming and boring, and when I post my solution after properly polishing it for a while, I'm a cheater... People on /sci/ aren't allowed to just be able to solve (some) Putnam problems or what?

>>4414630
I found the same thing, I don't see how he could be disqualified for using a relatively normal approach. In fact I don't see many others for the moment.

>>4414666
You have a tripcode only to show off with your math "skills". Arrogantly you brag by spamming the putnam threads with your [irony]great ideas[/irony] and in the end you google the solution because you are actually too stupid to solve it on your own. You are pathetic for needing the appreciation and recognition of a board that is based on anonymity.
tl;dr: You are what is wrong with /sci/.

>>4414687
Why wouldn't he want that? If you could solve stuff, you would want people to recognize your "ability" and not disregard your posts because they don't know who they come from.
That's clearly not what's wrong with /sci/.

>>4414690
I solve the putnam problems for myself most of the time. Then I don't post the solution. I simply wait for other anons to try, so I can help them and assist their steps towards it. Posting math knowledge with a fucking tripcode is the most pathetic thing someone can do and is ruining /sci/.
Why do I even argue with a goddamn tripfag? You'll just say some stupid shit like "u mad".

@ the tripfags:

1. drop the trip
2. don't cheat with google
3. don't post full solutions, post hints instead

>>4414697
well u probably mad but that's not the point. I mean you cannot blame anyone for anything they do in here, except probably for trolling and posting shitty stuff. As long as it is maths or science related and no one even makes money out of it, I don't see the problem.

>>4414704
no one fucking cheats with google, what's wrong with being able to solve simple putnam questions?

>>4414705
The purpose of these putnam threads is to discuss the problem and to find a solution together. It is not the right place for some arrogant aspie to google the solution, to put on a tripcode and to post ITT in order to say "Look at me, I are great mathematician durrrrr".

>>4414724
>google the solution
confirmed for retard. Or maybe Frenchies are genuinely better.

>>4414697
>I simply wait for other anons to try, so I can help them and assist their steps towards it.
That's nice. I hardly ever see anon taking a work in progress from someone else and adding/correcting it, though. Usually people post either:
- crap,
- a whole solution,
- their first step toward a solution,
but it's almost always independent from what the others did. The only cool discussions about how to tackle a problem that I remember were with mathfag, not with anon (though anon has proved able to do well on Putnam problems more than once).

>>4414704
>1. drop the trip
I only use the trip in the putnam threads or similar threads, I even delete and repost without the trip when I contribute somewhere else and forget to have it. But I like to have it here.
>2. don't cheat with google
Well I don't, but it's not like there's any way it can be proven (in either direction).
>3. don't post full solutions, post hints instead
It's actually a good idea. I'll do that from now on (at least when I convinced myself that I have the solution, because last time I wrote some kind of "hint", it was actually false...).

>>4414733
>I only use the trip in the putnam threads or similar threads
This is the wrongest place for a tripcode. While in normal /sci/ threads tripcodes can be useful to defend a position against trolls, in the putnam threads trolling is not a problem. Only the math counts and no recognition is required. Recognition is even bad in pure math threads. I think your posts have demotivated some anons and made them lose their interest in these threads.

>>4414743
I don't really understand why that would happen. Honestly what would be best is the ID system that is now on /b/, for instance. I haven't really played with it much but it does what I'd want: being able to recognize who's who within a thread. I don't really care about reputation from a thread to another. It's just helpful for the discussion to know who's who when you are working collaboratively.

>>4414755
4chan's most important concept is the idea of anonymity. It works when people collaborate, like they should and would in the putnam threads, if there were no tripfags interrupting the collaboration. The only reason to reject anonymity and to choose a name or an id is when trolls are imminent. You can use your tripcode for keeping up a conversation in any other /sci/ thread, but please not ITT.

>>4414755
I agree with that. /b/ is slightly improving, all of a sudden.

>>4414755
He's claiming efficiency, but his opinion is based off of no factual evidence, merely anecdotes.

By defending yourself you are already deviating from the original topic of the thread and are therefore being inefficient.

>>4414784
>4chan's most important concept is the idea of anonymity.
Being able to be anonymous is the main idea indeed. I still don't think that choosing occasionally to be named changes that. I mean, again, the ID system on /b/ does exactly what I'm trying to do here with my trip. I could use something more like an ID by just removing the name and switching trip in every new putnam thread. Assuming the other current tripfag also do it, that would make it kind of anonymous. I wouldn't mind that.

>>4414805
Or you can just drop the trip completely. The thread's topic is the putnam question. Mathematical discussion don't need any self-proclaimed authorities and a nice collaboration doesn't work with a guy who needs to cry "first".

>>4414818
I am saddened by the fact that you think that I think otherwise. I'm not claiming "first" or anything. And, again, I just like the fact that, at least within a discussion, people know which posts are from the same poster. Do you really think that having 3 or 4 people, among the anonymous posters, use a different ID in each putnam thread, would actually make the threads worse than pure anonymity? Maybe I'm not seeing it through, but I really don't think that would hurt. And I would gladly switch to this instead of the "named"-tripfagging.

>>4414834
The anons posting here can get along without being recognised. You on the other hand lead the thread into derailment. Once again: All that counts ITT is whether a posted idea is mathematically correct. This does not need a poster to be identified with the idea.

>anonymous
>derailing the thread
>accusing a trip of derailing said thread
you sir must be a biologist. Or a troll.

>>4414861
You can put your trip back on. No one is taking your samefagging serious.

>>4414846
Well hopefully WE won't lead any thread into derailment anymore if we end up with a way of doing things that satisfies everybody. You're saying that being able to identify a poster:
- Doesn't make the thread easier to read. I disagree: as soon as there are 4 or 5 anons posting, while the mathematical truth of a post is what matters, knowing who posted it helps understanding it faster, since you understand better what it refers to, what notations are used etc,
- Actually makes the thread worse. I can agree that identifiable tripfags from other threads could maybe annoy some. I'm not sure why exactly, but okay. But if the IDs are within a thread? I mean, consider that /b/'s ID system comes to /sci/ right now. Is that a bad thing? I don't think so. Why would it be bad? And if you agree it wouldn't be bad, then why is it so different to have some people with a random ID and some without?

implying I'm just not another anon who actually cares about /sci/

>>4414880
Then you should share my opinion.

>>4414879
I'm not against tripfags in general. A good reputation on the board can be a good thing. But not in the fucking putnam threads. At least not if you
1. spam huge amount of latex and expect others to read
2. post whole solutions to show off

A tripfag could have good reptutation in a putnam thread by being helpful without being a selfish aspie. TN5 has missed this opportunity.

That's the bad thing about tripfagging. Once some people hate you, they won't stop anymore.

>>4414901
>1. spam huge amount of latex and expect others to read
How is it not easier to read than the mathematical posts NOT done in LaTeX? I mean, seriously? I don't spam huge LaTeX formulas when there's no need for formulas to solve a problem. And I don't see you going on a crusade against anons or other tripfags using big formulas, when they do (and they sometimes do). I really, really don't think there's a problem with that.
>2. post whole solutions to show off
That's judging on mere intent... I'm thrilled when I'm able to solve a problem so maybe I'm showing off to myself. But "TN5" is a name I only have on /sci/ (since it's derived from the tripcode itself). It's not like I can brag about it or anything. If I wanted to brag, show off, or to build a reputation, I would post as TN5 in other threads too, not as anon.

>>4414928
You spam more latex than anyone else. Especially you post stuff that is wrong and correct it a hundred times by subequent posts.

>>4414955
>Especially you post stuff that is wrong and correct it a hundred times by subequent posts.
So it's bad when I post something that is wrong? Then why:
>>4414697
>I simply wait for other anons to try, so I can help them and assist their steps towards it.
Or should I let other anons correct it, because if I correct it myself, it's too much of me and it makes people think I'm megalomaniac?

>>4414967
>it makes people think I'm megalomaniac
Yes, although I'd prefer "autistic" and "narcissistic" over "meglomanic".

Post your idea, make it short and make sure what you post is correct.
It's our thread, not yours alone.

>>4414979
Okay. I'll try to make shorter posts and to proof-read them more. Do you consider >>4414610 too long though? I mean... I can skip a few steps, but then it's not as easy to read anymore.

>>4414990

>>4414610 would be okay, if it wasn't so close to google's solution.

>>4414996
If you really attempt the Putnam problems like you say you do, you know that it was the basic way to go. There are problems in which the "simple" approach does not work, and in these, it could have been suspicious. Here, the candidate is supposed to go that way first, and to notice that it works. There's no reason to look anywhere else. It's like, you're asked to prove that a series of positive reals diverges, you notice that the term doesn't go to 0, why bother proving something more complicated?
But ok, independently from the "did he cheat? did he not cheat" discussion which isn't really more interesting than the science vs religion threads, I get your point and I'll try to be less verbose in my proofs / proof attempts.

>>4415016
Okay, thanks for your cooperation.

Hey guys is this the newest TN5 sticky?

You do realize Harvard lost it's rights to associate itself with math and science when it pressured it's dean to resign after commenting that a difference in IQ standard deviation between males and females meant less female geniuses to participate in math/science right?

>>4415405
its

>>4415405
Yeah, seriously. Politics, ethics, and how lobbies handle what they consider communication errors: those are the most important things in a maths school. Why would we care about, like, maths, or science?

Say someone were to PROVE that free will is an illusion, and that everything has been predetermined.

Why is it that, deep down, we'd still live, and think with the notion that our actions have merit?

I'm not asking for a debate if determinism is correct. What I'm asking is, why would we, as we currently are, be unable to drastically change society?

tl;dr Neurologically, why do we still believe, subconsciously, in free will thinking process?

>>4415953
If you just give up, you're merely demonstrating that you were predetermined to be a loser.

>>4415959
Sorry, I was predetermined to accidently post here instead of making a new thread.