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/sci/ - Science & Math

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File: 39 KB, 425x600, pi.jpg [View same] [iqdb] [saucenao] [google]
6748294 No.6748294 [Reply] [Original]

this was posted on /b/ in a troll science thread. but doesn't it pose a serious question?

>> No.6748299

>>6748294

You will never reach a true circle as you progress like that picture does. You can't actually repeat to infinity. If you "stop" at any point then you will end up with some polygon with a huge number of edges and vertices.

>> No.6748302

>>6748299
you're right, I'm a dummy. thanks

>> No.6748313

The slope of the edge of your polygon is constantly alternating between 0 and undefined.

As points and lines are infinitely small, if you zoom in on your finished "circle", you'll still see the zig-zagging of the straight lines and you can never make them small enough to approximate circumference.

Though these little jagged edges are small, theres so many of them that their length adds up, and the total extra length ends up being about 0.85...

>> No.6748346

>>6748313

You mean 0.86

Fucking niggerfaggot

>> No.6748347

>>6748346
why .86?

>> No.6748348

>>6748347
3.14

>> No.6748351

>>6748294
doesn't mean shit you could put an nearly infinitely long line INSIDE the circle and have it look just like a circle to human eyes.

>> No.6748416

>>6748348
pi is over 3.14, so the difference is under 0.86, hence the ... in the original answer, retard.

>> No.6748434

>>6748299
>You can't actually repeat to infinity
In math you can.

>> No.6748436

>>6748313
>infinitely small
>you'll still see the zig-zagging

Doesn't understand infinity

>> No.6748438

>>6748434
Repeating to infinity isn't normal.
But on math it is.
>not even once

>> No.6748439

The limit of a function as it approaches a point is not necessarily the same as the value of the function at that point.

The limit of the length of a sequence of polygons that approach a curve is not necessarily the length of the curve.

The length of a curve is, in fact, defined as a limit of straight-line figures, but there is a condition added that is necessary to make lengths consistent. Do you know what it is?

>> No.6748442

>>6748436
http://en.m.wikipedia.org/wiki/Taxicab_geometry

>> No.6748443

>>6748439
TL;DR
shape =/= length

>> No.6748445

In a base-pi system, pi is 10.

>> No.6748448

>>6748442
>http://en.m.wikipedia.org/wiki/Taxicab_geometry

"This page has some issues"
m-muh feelings

>> No.6748450

>>6748442
>http://en.wikipedia.org/wiki/Taxicab_geometry

fix'd and good post anon.

>> No.6748453

>>6748294
The perimeter is still 4 after a gazillion billion steps, but as it happens, infinity isn't a number and there isn't a step that is second to last in the process that ends in infinity, nor is there that last step.
So when you make the unavoidable warp into infinity, the perimeter becomes, not a jagged line, but a circle.

>> No.6748461

>>6748453
>>6748443

So, at infinity, the perimeter is 4 and yet it is a circle.

>> No.6748491

<span class="math">Test[/spoiler]

>> No.6748503

>>6748461
the zigzagging edge doesn't disappear at infinity

>> No.6748508

>>6748503
1/x isn't zero at infinity

>> No.6748509
File: 266 KB, 241x238, chuckle.gif [View same] [iqdb] [saucenao] [google]
6748509

>>6748434
>In math you can.
this is what mathematicians actually believe

mfw

>> No.6748514

>>6748509
it's easy to agree you're not one

>> No.6748519

>>6748299
>You can't actually repeat to infinity.
You can.
It's just that the corners do not converge toward the circle, but another shape.

>> No.6748520

>>6748519
right... bunny ears?

>> No.6748525

>>6748294
you imply :
limit of lengths = length of the limit

wich is true only if the derivative curve converge to the derivative curve of the circle.

PS : the curve DOES converge toward the circle , those who said otherwise are middle schooler, or failed high schooler

>> No.6748530

>>6748520
I think it's more in fractal tier stuffs, considering some of them have a particularly interesting perimeter compared to their repartition in 2D space.
Koch snowflake for instance has infinite perimeter, while being bounded in R2.

>> No.6748535
File: 45 KB, 533x400, mathematicians.jpg [View same] [iqdb] [saucenao] [google]
6748535

>>6748514
"actually, what we have calculated is wrong but when we apply the axiom of infinity everything is correct"

>2014
>believing in the existence of infinity
>thinking infinity is all-knowing, all-wise and its ways are mysterious
>thinking we get our knowlege out of a pool of infinite answers
>thank infinity that it made our knowlege possible before going to bed
>thank infinity, that it gave us something to eat
>Cantors writings are the bible
>worship the concept of cardinality

while that happens:

>not knowing about the illusion of free will
>not knowing that that our senses and how we are build makes everything finite in the first place
>still assume infinity even if every logical proof is impossible to be complete.

The worst thing about this is that I have to live with this people on the planet. They just as are worse as christian fundamentalists.

Rigor everywhere but when it comes to infinity suddenly no one need it.

mfw infinity

>> No.6748539

>>6748525
Well fuck. I apologies for being retarded, I was >>6748519 and >>6748530
> those who said otherwise are middle schooler, or failed high schooler
No I'm not. I'm just getting back at math being lazy for the whole holidays.

Also http://qntm.org/trollpi really explains it quite well.

>> No.6748587

>>6748535
>yadayadayada
time for an adderall

>> No.6748651

The tangent of the curve is undetermined, whereas the curve of a circle is.

>> No.6748652
File: 58 KB, 1150x966, Trolling of idiots.png [View same] [iqdb] [saucenao] [google]
6748652

>>6748294
>but doesn't it pose a serious question?

>> No.6749402

>>6748416
<span class="math">4-\pi\approx 4-3.1415 = .8585\approx .86[/spoiler]

>> No.6749466

No matter oh many steps you take it is still stepped. It is not the same as the curve. The whole point of a continuum is that you can continue steps line these infinitely and it will always be jagged. If that was not true, then it would not be a continuum.

>> No.6749467

>>6748313
I am gonna need some proof for these claims.

>> No.6749471

>>6748652
No, you.

>> No.6750497

>>6748313
>The slope of the edge of your polygon is constantly alternating between 0 and undefined
wat?
rest is understandable

>> No.6750517

>>6748491
Wh-wh-what?

>> No.6750533

>>6749467
The proof is in OP's image, such a progression can't approximate a circle. Just because something looks like an approximation doesn't mean it is one.

>> No.6750648

A friend claims he made this troll picture years ago.
The circle at the end isn't really a circle, it's an "infinigon".
You can make all kind of infinigons, another example is this one right here >>6748652

>> No.6752137

integrals

>> No.6752141

>>6748434
and when you repeat to infinity you still have a zig-zag border

>> No.6752242

>>6752141

>>6748508

>> No.6752257

>>6748294
No, because that sequence of shapes doesn't converge to anything.

>> No.6752262

>>6748294
this is posted daily here and has been for years. The answer is simple but requires babby knowledge in analysis and topology. /sci/'s userbase is for the great part far from satisfying these criteria.

The solution, of course, is that the troll is assuming that the length functional is continuous with respect to the topology on path-space in which the paths given converge to the circle, which is evidently false.

It baffles me that people think that the limit of a function is the function of the limit, with no hypotheses on the function.

>> No.6752270

I'm too lazy to read through and see if anyone has posted the right answer so this is it:

As you continue that pattern the area of your shape approaches that of a circle, but the perimeter of your shape does not approach that of a circle.
/thread

>> No.6752336

>>6752262
>assuming that the length functional is continuous with respect to the topology on path-space in which the paths given converge to the circle

Which implies you can't ever trust a limit you
generate after your Calculus classes unless you also have a degree in Analytical Topology.

So you need an IQ of at least 130 - 135 to get into and confidently use the calculus.

>> No.6752466

>>6752336
what the fuck are you high on? What does anything you said even mean?