Disprove this

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

>>still get 30+ answers
>only 10 replies

this board is supposed to be populated by smart people

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

just wait, fgt

>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].

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

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.

This is the right answer.

that would give you a diamond with a perimeter of 4

>falling for the obvious four factorial part of the troll

We haven't even gotten started

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.

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

yep

you have proved that
pi

lol

bumping so post gets 30+ replies

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

cause youre a fucking faggot

Curves are just a perspective illusion.

>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.

Courage the Cowardly Dog was a freaky show

No one ever said the corners had to be square.

30th post

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

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

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

nice try OP

you almost got the right answer

en.wikipedia.org/wiki/Arc_length#Definition_for_a_smooth_curve

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

see also 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

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

www.youtube.com/watch?v=D2xYjiL8yyE

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.

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

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

46 posts, nugger

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

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.

it is continuous in the C1 topology :^)

Look at all the kids that haven't taken calculus. So cute...

kek

0/0 is 1? Prove it.

Kek

Well, at least you got the 24 part right.

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".

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
web.math.ucsb.edu/~jcs/SqueezeTheorem.pdf

Also
>THE HOSPITAL

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

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?

no you're just doing it wrong

you have proved that
pi

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

Dude Veeky Forums is full of fucking retards

pi is 4 at the center of a black hole

Learn analysis man

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

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

You can't apply limits to everying brinlet.

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