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/sci/ - Science & Math

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10852531 No.10852531 [Reply] [Original]

holy shit...

>> No.10852554

there's another way to do this where Pi equals 2

>> No.10852585

https://en.wikipedia.org/wiki/Modes_of_convergence_(annotated_index)

>> No.10852590

>>10852531
You're approximating the area of the circle by doing that, not the length.
The curve and the circle have the same area but it's clear that they have different lengths.

>> No.10852591

>>10852531
Kek

>> No.10852595

>>10852531
>4!
pi is not 24

>> No.10852599
File: 757 KB, 480x208, this-is-impossible.gif [View same] [iqdb] [saucenao] [google]
10852599

>>10852531

>> No.10852605

Okay, so imagine after folding the corners, you draw a straight line starting from where the outline meets the circumference and touches the opposite side of the box. Now you have a shape that has a smaller perimeter than the box, but still larger than the circumference.

>> No.10852607

>>10852605
>he doesn't know about limits
I feel sorry for you

>> No.10852609

>>10852605
>and touches the opposite side of the box
What did you mean by this

>> No.10852618
File: 2 KB, 203x191, hypotenuse length.png [View same] [iqdb] [saucenao] [google]
10852618

>>10852531
distance =/= length

hypotenuse length, [math] n \rightarrow \infty [/math]

a+b or [math] \sqrt{a^{2}+b^{2}} [/math] ?

>> No.10852702

>>10852531
That's how engeneers keep steel for home projects.

>> No.10852714

>>10852531
making the horizontal and vertical stairways infinitely small still doesn't make them a circle. they're still stairways, just infinitely small ones.

this seems related to the infinite coastline paradox.

>> No.10852750
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10852750

>>10852609
Well, draw a diagonal through each of the corners w/o going into the circle . That hypotenuse should have a smaller length than the combined lengths of its perpendicular sides, so the trimmed shape should also fit inside the square perimeter and still contains the circle. I'm pretty stupid, so I don't have a clear explanation for this.

>>10852607
I don't think you need to understand limits to get the point I'm trying to make. How would limits work here?

>> No.10852759

>>10852531
Shouldn't the corners cut INTO the circle to mantain an equivalent area?
Do you want pi or the ribbon wrapped around pi?
This is stupid.

>> No.10852761

>>10852714
>infinitely small ones
so, a circle

>> No.10852765
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10852765

>>10852750
>How would limits work here?
how indeed

>> No.10852769

>>10852595
HahahahahahHaAha classic STEM joke rofl Cause ! means factorial hahahaha lmao

>> No.10852775

>>10852761
no, still stair-steps.

>> No.10852783

>>10852765
Well, if you need help see

>>10852618

>> No.10852785

>>10852775
at any finite number, stair-steps.
at infinity, it's perfectly smooth.

>> No.10852913

>>10852785
only if you're thinking in pixels on a screen. in reality a jaggedy shape stays jaggedy, no matter how tiny you make it, including infinity. infinite detail doesn't transform one shape into another.

>> No.10852922
File: 132 KB, 778x463, PepeVentsFartToFren.jpg [View same] [iqdb] [saucenao] [google]
10852922

>>10852531
> taxicab geometry

>> No.10852949

>>10852913
whoosh

>> No.10852953

>>10852750
Take any pattern like that (with diagonals) and repeat it. You get a number for 'pi' between pi and 4.

>> No.10853022

Just because it appears like the result of a sequence, does not make it part of said sequence.

>> No.10853148

>>10852531
Pi is a variable, not a constant

>> No.10853157
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10853157

>>10852531
what is the resolution to this paradox? nobody has actually proved it wrong

>> No.10853187

>>10852785
think relatively.
no matter how much you zoom in, you will still see that the circle is smooth and the box has corners.
circle allows you to zoom in as much as you like, because pi is irrational. at some point you will see the circle like a straight line, but those stairways will always be in that shape, it doesn't matter how much you zoom in, you can't get a smooth stairways, it's not possible. there's always those extra length.

>> No.10853389

>>10853187
this. chopping the corners infinitely still gets you a shape with corners, therefore it cant be the same as a circle

>> No.10853395

>>10852531
A circle doesn't have a length.

>> No.10853432

>>10853395
Why do namefags always say the stupidest shit

>> No.10853435

>>10853432
Why do anonymous posters think that their opinion adds to the communal gestalt?

>> No.10853440

>>10852531
https://www.quora.com/How-does-one-explain-the-pi-4-%E2%80%98proof%E2%80%99-regarding-a-square-reduced-to-a-circle

lol quora > sci

>> No.10853621

>>10853157
multiple anons have already proved it wrong, but to state it succinctly: the sequence does not converge to the circle in the C1 topology. Since the definition of arc length involves a derivative, one cannot conclude that the arc length of the limit is the limit of the arc lengths.

>> No.10853629

>>10853440
the first answer is mostly a cop out - it doesn't even use the word differentiable

>> No.10853634

>>10852531
That will never make a circle.

>> No.10853702

>>10853157
>what is the resolution to this paradox? nobody has actually proved it wrong
1) The circumference of the circle is ~3.14. The perimeter of the square is 4. The spaces in between the two shapes have a total area of ~.86.
2) The circumference of the circle is still ~3.14. The perimeter of the folded square is still 4. The new spaces in between the two shapes still have a total area of ~.86.
3) Repeat this as much as you want, but the spaces never lose any area. What happens is you just decrease the space per corner while increasing the number of corners in a way that always preserves the total area of ~.86.

>> No.10854185

>>10853157

As you make the corners smaller you change their scale. Smaller scales, smaller measurements. Its a limit problem. The Universe is geometric like this, squares, but its also comprised of scale factors.

>> No.10854246

>>10853435
gas yrself fgt

>> No.10854297
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10854297

>>10853157

>> No.10854312

>>10852531

Thank you OP for again demonstrating that the concept of infinity is pants on heads retarded.

Although many of the brain dead wipes who frequent this board will not understand your point.

>> No.10854351

>>10854312
>demonstrating that the concept of infinity is pants on heads retarded

how does it do that?
Infinite removal of corners isn't necessary for the image to retain its meaning, it only needs to be done enough times to look like a circle

>> No.10854385

>>10854351

Scale changes. Different scales different measurements. No one figured this out. No one figured out everything. Spend $200,000 at Uni

>> No.10854389

>>10853187
>let's pretend finite is infinite

>> No.10854414

>>10852769
glad you liked it

>> No.10854437
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10854437

>>10854351
>Infinite removal of corners
IMO, the wrongness of this pi=4 result is most concisely demonstrated by calling it "infinite multiplying of corners." A circle doesn't have any corners.

>> No.10854725

>>10853157
"circles", as in a series of infinite points which are equidistant from a single point don't exist in the first place.

>> No.10856222
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10856222

Circle of diameter D
>D = 1m
outside the circle is tangent a single SQUARE of side L
>L = 1m
The RATIO perimeter/length is PI (no dimensional units: [meter/meter]= [1])
PI=P/D=[4 m]/[1 m]= 4 (no units)

>PI=4
I MADE IT
Now you make the pentagon

>> No.10856230

>>10852531
>table = 4
I don't get it