/sci/ - Science & Math

[Anonymous No.3230227]

hey /sci/
i know you've seen this pic a million times, but i need to know why it's not true. Does the perimeter converge to pi?

[EK !EKFQOBUFnQ No.3230232]

you can't do it 'to infinity'
the corners will still be spiky, not a smooth curve like a circle.
so the cicles circumference is pi (real pi, 3.141...etc)
and the spiky 'almost a circle' distance is 4.

[Anonymous No.3230231]

Nope, still four.

[Anonymous No.3230242]

>>3230232
wat
are you silly or something?
that doesnt explain shit if they say "to infinity", why would there still be spikes in the limit?

[Anonymous No.3230246]

>>3230242
The spikes would be infinitely small, but there would be infinitely many of them.

[Josef !!nUf2NflSAyw No.3230249]

The area will converge to the area of the circle, but the perimeter won't.

[Anonymous No.3230253]

>>3230232
My god your maths education is horrible...YES you can do it to infinity and yes the jagged perimeter actually can be made to converge UNIFORMLY to the perimeter of the circle. The reason why it doesn't work is simply the fact that there is no connection between convergence of one curve to another and convergence of length of one curve to length of another curve. OP's pic can in fact be seen as such a counterexample, and that should be clear from the beginning. The value of pi by the definition as the circumference of the circle can easily be established and shown to be NOT four, after that anything which shows that it somehow "is" four must contain a mistake; but since it's more or less possible to approximate any given smooth simple closed curve by a family of curves of fixed length (proof goes through using the Jordan curve theorem which one proves using the Mayer-Vietoris sequence for compactly supported de Rham cohomology) it means that the assumption that pointwise (or even uniform) convergence implies convergence of their lengths is WRONG. And that's all there is to it.

[EK !EKFQOBUFnQ No.3230254]

>>3230242
the method in each step is cutting out the corners. even doing this to infinity (this is basically meaningless anyway, but i'll go with it...) will mean it has to be spiky, because it is spiky after every single step, and HAS to be spiky considering the method you are doing (cutting corners) but a circle isn't spiky at all, it is perfectly smooth.

[EK !EKFQOBUFnQ No.3230258]

>>3230253

[Anonymous No.3230260]

>>3230254
of course you can do it to infinity, lol.
like in your picture, it's just the limit of a sequence of functions (that even converges uniformly to that smooth line of yours)

[MR. RAGE !D9l9S8Lio6 No.3230261]

TAXICAB GEOMETRY, NIGGA.

EDUCATE YO'SELF.

[Anonymous No.3230263]

>infinity thread

[Anonymous No.3230264]

>>3230254
Read >>3230253, and please go revise your basic calculus, it's a shame to see a supposed zoologist not know the definition of a limit.

[Anonymous No.3230271]

>>3230253
it's >>3230242 and >>3230260 here. that makes more sense, thanks.

[Anonymous No.3230281]

>>3230254
>>3230258
This is brilliant. Just minutes ago I hear EK talk in another thread how this "morning" (wherever it (yes you EK, it) is) /sci/ is riddled with idiots/morons. And now this, how on fucking earth is it possible that something that claims to study zoology doesn't even know the definition of a limit?!

EK OFFICIALLY CONFIRMED FOR NOT KNOWING SHIT ABOUT ANYTHING AND HAVING LIED ABOUT ITS ZOOLOGY STUDIES.

[EK !EKFQOBUFnQ No.3230287]

>>3230281
zoology =/= maths

[Anonymous No.3230294]

>>3230287
i guess i wont get a true enough answer
was i just trolled? or did you really not know what you said here >>3230232 and here>>3230254 is complete bullshit?

[Anonymous No.3230298]

>>3230287
Seriously, that's your response? So you're all for not doing even basic calculus in your studies? Don't be fucking silly, all the haters saying biologists/zoologists don't know any maths will suddenly be right and zoology wouldn't be considered a proper natural science anymore but pseudoscience like the rest of humanities. DO yourself a favor, get off 4chan and go revise those calculus exercise sheets. Or hey, here's an even better idea: don't do that, and just stay out of every math thread ever so that other people don't have to come in every time to clear up the mess you've made with your uneducated explanations of mathematical phenomena. But for now I suggest you GTFO.

[Anonymous No.3230300]

>>3230287

EK = troll

It are zoology and maths.

[Anonymous No.3230301]

The black perimeter isn't circular because no matter how many times you repeat, it's only tangent to the circle at 4 points

[EK !EKFQOBUFnQ No.3230304]

>>3230294
>>3230298

my explanation is right. this is basically obvious anyway seeing as pi clearly doesnt equal 4.
secondly, even if i wern't good at maths, im only 1 individual. this wouldnt prove that ALL zoologists arnt good at maths.

the corners ARE still spiky. the method of cutting corners to form the next step can't possibly form anything smooth.

[Anonymous No.3230311]

>>3230304
Now you're just trolling, seriously. If not, I urge you to read >>3230253. And no, your explanation is NOT right at all, since its based on a very false assumption (also addressed in the above referred post).

[EK !EKFQOBUFnQ No.3230320]

>>3230311
i'm not trolling. it DOES NOT form a curve, it is still only comprised of an infinite amount of infinitely small horizontal and vertical lines.

[Anonymous No.3230323]

>>3230304
do you really not know what "to infinity" means?

[Anonymous No.3230330]

>>3230320
no it's not, EK. I'll be probably the tenth to suggest you go read your introductory calculus text book.
>inb4 HURR I TROLL YOU
no, acting moronic is not how one trolls.

[Anonymous No.3230333]

Reason and proof:

pi is not the circumference of a circle. pi is the ratio of a circle's circumference to its diameter.

C = pi * d,

pi = C / d.

[Anonymous No.3230338]

>>3230333
no my dear, diameter was assumed to be 1 so pi is circumference of such a circle. for a detailed explanation check this guy >>3230253, he seems to know what he's talking about.

[Anonymous No.3230343]

>>3230320
I suppose you haven't heard of integral calculus. "Those bars! They are BARS! THEY CAN'T BE CURVES! FUCK THIS SHIT"

[Anonymous No.3230348]

Oh god, I wish I screencapped that post where EK said she didn't fail at math and grammar.

[Anonymous No.3230359]

>>3230348
+1, would be an excellent time for posting it, seeing as she started to write like a 12 year old up there and proposed some ridiculous mathematical concepts.

[Anonymous No.3230386]

nobody would give half as many shits about EK's answer being cruddy if she wasn't a tripfag
just pointing that out... you're all kinda fanning the flames

>>3230253
>>The reason why it doesn't work is simply the fact that there is no connection between convergence of one curve to another and convergence of length of one curve to length of another curve.

so... is there not really any explanation for this discrepancy other than the fact that it gives a different result?

that's... unsatisfying

[Anonymous No.3230410]

>>3230253
You're retarded.

So, going by your post, if the Greeks first did OP's method, then pi would be 4, and anyone who said pi is 3.14 would be wrong.

Precedence in mathematics is of no value at all.

[Anonymous No.3230418]

EK's answer is correct even if it wasn't explained very well, are you all idiots or something?

[Anonymous No.3230430]

Im no mathfag, actually im pretty retarded when it comes to math, but wouldnt this just happen?

just sayin

[Anonymous No.3230434]

>>3230386
>so... is there not really any explanation for this discrepancy other than the fact that it gives a different result?
There is of course an explanation, you just have to look at the definition of the length of a curve (and consequently the definition of Riemann integral) and the definition of uniform convergence. You will see that there is no obvious connection at all (in fact none) and with many counter examples (including OP's pic) you see indeed that there is no causal relation.

>>3230410
>So, going by your post, if the Greeks first did OP's method, then pi would be 4, and anyone who said pi is 3.14 would be wrong.
Can you quote the exact passage where I supposedly said that? See, there was a reason I put the "is" between quotation marks. pi is defined as the ratio of the circumference of a circle to its diameter. All I said is that attempts to define it alternatively through the limit length of a sequence of curves might lead to a contradictory result (like in OP's pic), and that furthermore if one applies enough thought one will realize that a definition through the limit length of a family of curves is in fact ill since one can choose the family so as to get an arbitrary result. I see /sci/ is neither strong on math nor on reading comprehension today.

[Anonymous No.3230437]

I've seen a similar construction with the diagonal of the unit square by making it into a "staircase" with length 2. Even at infinity, the length is still 2, instead of sqrt(2).

That's dangerous thinking. People get tossed over boats for ideas like that.

[Anonymous No.3230438]

>>3230227
>i need to know why it's not true.
It might be true for YOUR circles, but MY circles are made of infinitely fine pie-slice triangles.

[Anonymous No.3230443]

It's cause the perimeter is black.

Fucking darkies always fucking shit up.

[Anonymous No.3230450]

If you inverted the corners, then found the hypotenuse between the corners, then you'd be reducing the perimeter and using the right method.

[Anonymous No.3230455]

>>3230333
Fucking this, I don't know why you guys are arguing hard about this. The picture shows the circumference of circle not the pie.

[Anonymous No.3230457]

[Anonymous No.3230463]

This is simple.

A circle is where there is a constant radius around the circumfurence. If there are infinite spikes on the circumference then it is not a circle. Then the pi rule does not apply.

So obvious. You're all amateurs.

[Anonymous No.3230494]

>>3230457

Man EK.... When will he/she learn?

[Anonymous No.3230544]

>>3230418
Actually, it depends on your axioms. There's more than one way to set up math.

This kind of model of curves, with arbitrary infinitesimal texture, has got some obvious real-world parallels. While the analogy of macroscopic to microscopic features isn't perfect with real-scale to infinitesimal-scale features, it is good enough to work with.

Imagine this as a function, though. In every other way identical to a (half-)circle, integrates to the same value, but differentiable nowhere (this is, of course, using a different definition of differentiation than the common one, based on limits, although the inventors of calculus would have no trouble following this line of exploration). You could make different kinds of differentiation, based on throwing infinitesimal particles on it from different angles: it would answer both "Horizontally flat?" and "Vertically flat?" with "Yes!" But you apply "macroscopic differentiation" and you get the usual smoothly changing slopes.

You should be able to see both how this kind of model has its own self-consistent logic (and real-world relevance), and how it conflicts with the usual models of calculus and geometry.

[Anonymous No.3230550]

>>3230320
EK are you still here? I am posting this anonymously even though I am a tripfag because I know I would pay a social price for what I want to say. I just want to say I love you. I dream of you. I love you so much.

[Anonymous No.3230671]

>>3230544
Oh... it just occurred to me that you could set it up to have a probabilistic model of differentiation. When you throw an infinitesimal particle at a point on the curve, you could describe the probabilities of various angles of reflection off of the curve's infinitesimal surfaces.

[Anonymous No.3230683]

Pi is not 4, therefore this doesn't work.

[EK !EKFQOBUFnQ No.3230981]

>>3230457
>EK idiocy #001.png
lol, looks like you are planning to make a lot of those.
heh, have fun =p

>>3230550
yes hello. and thankyou :)

[Anonymous No.3230984]

The length of the curves in a series does not necessarily equal (or even converge) to the length of the limit curve of the series.

Sorry.

[Anonymous No.3231008]

Whats going on in this thread?

[Anonymous No.3231019]

>>3230227
The only time when the hypotenuse of that triangle is the same length as the other two sides is when all lengths are zero. Then you have to divide the perimeter by those zero lengths.
You can't divide by zero, nig‌ger. When you try it you get ridiculous bullshit like 0 = 1 or 4 = π.
This is exactly that same problem, just hidden a little more.

[Anonymous No.3231050]

>>3230683
You are the meaning of stupid.
OP told you that. he asked why the argument is not valid.
You answered by saying "Because the result is wrong."

[Anonymous No.3231067]

It's wrong because i say so!

[Anonymous No.3231068]

>>3231050
When the result is wrong, it proves the argument to be invalid.
4 ‌≠ π.
Any argument ending in 4 = π is therefore false by contradiction.