Disprove this

>he doesn't know .9999999=1
Top zozzers m80

You will never get a circle, because you will always have corners left. Nice try brainlet.

>>8558266
>repeat to infinity

Found it. It's never a perfect circle.

>>8558275
>It's never perfect
Damn why am I getting in feels about this fucking shitpost

File: this is what brainlets believe in.png (7KB, 297x279px) Image search: [Google]

7KB, 297x279px

>>8558266
>repeat to infinity
you'll get shape in pic related

>>8558281
>the perimeter of which is still 4
Lol when will /sci/lets ever learn?

>>8558266
An infinitely zigzaggy line is not the same as a curve.

>>8558277
https://www.youtube.com/watch?v=0AXseEnXtsc

>>8558266
The sequence of n-gons as n goes to infinity is converging to the circle in area, but the boundary of the n-gon is not converging to that of the circle.

>>8558266
>you can't.
You're right. mathfags only use "limits" when it's convenient for them. they're perfectly fine with sin(0)/0 = 1, but oh no, you can't approximate a circle like this, it's too problematic for them!

>/sci/
>repost retarded troll pic from 2013
>still get 30+ answers
this board is supposed to be populated by smart people

>>8558361
>>still get 30+ answers
>only 10 replies

this board is supposed to be populated by smart people

>>8558266
You can't define a circle in the L1 norm, so the problem is an ontological contradiction.

>>8558376
just wait, fgt

>>8558394
>look mom, I used a dirty word on the internet!!!

In the space of piecewise differentiable curves, {f : [0,1] -> R2} with the uniform norm topology, the arc length functional is not continuous, it means that lim L[f] doesn't need to be equal to L[lim f].

>>8558266
1. you half the error of each line segment but double the number of line segments so the total error is still the same
2. dont write 4! write 4. pi is definitely less than 24

>>8558332
You can't divide by zero.

The limit of the picture is truly a circle. Yet with any natural amount of steps the length is 4.

>>8558416
This is the right answer.

>>8558266
that would give you a diamond with a perimeter of 4

>>8558422
>falling for the obvious four factorial part of the troll

We haven't even gotten started

>>8558266
for those who don't know:
the line does converge perfectly to a circle, but even if a line converges pointwise to another line, it doesn't mean the path length is the same.

>>8558416
>the arc length functional
What is the arc length functional?

>>8558416
>>8558426
yep

>>8558266
you have proved that
pi <= 4
congraz

>>8558792
lol

bumping so post gets 30+ replies

>>8558423
>You can't divide by zero.
Maybe YOU can't.

>>8558277
cause youre a fucking faggot

Curves are just a perspective illusion.

>>8558266
>two things look the same, therefore they are the same
thx op

Assume you have a mostly straight curve and you want to estimate the length of the curve, you can either use the euclidean distance between the endpoints which will give you a pretty good result, or add up the horizontal and vertical distances between the endpoints which will vastly overestimate the curve. You are basically repeating the latter error infinitely many times.

>>8558319
Courage the Cowardly Dog was a freaky show

>>8558281
No one ever said the corners had to be square.

30th post

>>8558422
>The circumference is 4!
Poe's Law 2.0, when syntax becomes semantics.

>>8560015
>when syntax becomes semantics
Or rather syntax is confused for semantics.

>>8558266
Move horizontally from any point in a circunference, you are no longer in the circunference.
Move horizontally from a point in that shape, you are still in the shape.
Both figures can not be equal.
QED

File: pi is an algebraic number.png (19KB, 750x776px) Image search: [Google]

19KB, 750x776px

nice try OP

you almost got the right answer

>>8558727
https://en.wikipedia.org/wiki/Arc_length#Definition_for_a_smooth_curve

>>8558679
>converge perfectly
never heard of that type of convergence. do you mean "converges uniformly"?

see also >>8558416
very neat and concisely summarized, altho for non-math fags it might sound a bit cryptic.

L(f) = length of curve f

lets denote the sequence of constructed curves in the op as f1, f2, f3, ... fn, ...

the important bit is that
lim L(fn) need not be the same as
L(lim fn)

in this case

lim fn = perfect circle
(uniform convergence)

and
L(lim fn) = L(perfect circle) = pi

however
lim L(fn) = 4 obviously

>>8560154
yes, converges uniformly. but that means nothing to the layman who gobbles up vihart's nonsense videos, who is told there's some jagged line upon "zooming in"

Pi is 4, not 24

>>8558266
www.youtube.com/watch?v=D2xYjiL8yyE

>>8558266
If Pn is the nth iteration of the polygone, your are wrongly assuming that:
lim(perim(Pn)) = perim(lim(Pn))

PS: for all the brainlets lim(Pn) IS a PERFECT circle.

>>8558294
You won't ever actually create a circle. Imagine rotating a square through itself to a diamond. You never create a circle.

>>8558416
Thank you anon for finally making me know the right answer after all this ViHeart shitposting.

>>8558397
46 posts, nugger

>>8558266
if you do it infinitely, you have to account for -1/12

>>8558266
The functional that maps a curve into a path length is not continuous. Hence, two curves may be arbitrarily close, but their path length is not required to be close.

>>8561456
it is continuous in the C1 topology :^)

>>8558274
>>8558275
>>8558281
>>8558319
Look at all the kids that haven't taken calculus. So cute...

>>8561341
kek

>>8558332
0/0 is 1? Prove it.

>>8558792
Kek

>>8560216
Well, at least you got the 24 part right.

>>8560199

Oh god this is Vihart's meme?
I can't fucking stand that cunt. She made some fucking awful video about the election and crying about the results and then proceeded to make a lot of unfounded arguments as to why she thought the Dems lost and then went full bleeding heart lib.

Not one for politics, but Jesus Christ if you are gonna talk about politics at least fucking know something before you make a god awful video. Math major or not, she's an absolute fucking retard for thinking she could walk into the subject uninformed and be like "lmao but statistical distribution and basic concepts explain this very complex issue".

>>8562500
0/0 could be anything, but in the case of
[math] f(x)= \frac{sin(x)}{x}, f(0) = \frac{sin(0)}{0} => \frac 00[/math]
There are a multitude of ways to show that f(0) = 1
Squeeze theorem is easily the most succinct
http://web.math.ucsb.edu/~jcs/SqueezeTheorem.pdf

Also
>THE HOSPITAL

>>8558361

A few maybe, but /sci/ is mostly used by /pol/ as a relief valve for shitposting about race and iq, climate change, etc.

>>8562708
Report and ignore those threads you dummy. sqt, math general, and any other actual question related threads are pretty good. ANY thread that starts with the OP "telling" people something is hint of a shitpost.

So is this why whenever I try to derive the area of a circle using a square root and x instead of cylindrical coordinates, I get a wrong answer?

>>8562897
no you're just doing it wrong

you have proved that
pi <= 4
congraz

TOP KEK

Integrating with respect to dx is fine when calculating area, but you need ds for arclength.

>>8558361
Dude /sci/ is full of fucking retards

pi is 4 at the center of a black hole

>>8563538
Learn analysis man

>>8562897
>using a square root to derive a circle
really made me think

>>8563555
It's been infiltrated by /pol/tards for some time. That's why you see all these threads about race, memedrives, women, jews, etc.

>>8561536
You can't apply limits to everying brinlet.

File: 3ifdamr.png (43KB, 259x224px) Image search: [Google]

43KB, 259x224px

>>8561536
Calculus is based on geometrical coherence and aplication, not pseudofractal "logic" like OP's picture, duh.