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/sci/ - Science & Math

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7060014 No.7060014 [Reply] [Original]

Why isn't Pi 4?

I know this image is a comic and it's not true. But why isn't it?

Infinity and Pi are both theoretical numbers.

If you would go to infinity, you would reach 4. Not 3.14 or something.

>> No.7060016

http://qntm.org/trollpi

>> No.7060019

>>7060016
But that still doesnt explain anything.


I know Pi is 3.41 or something, but im wondering why it wouldnt be 4


Look, for this you ll have to understand the principt of infinity. If you would do it till infinity, you would ultimatemly reach 4, right?

>> No.7060021

>>7059854

>> No.7060022

>>7060019
Of course we can never reach infinity, but theoretical, it is 4. But practical, it usually is 3.41 because circles are never 100% even.

>> No.7060024

>>7060019
no it does not converge to a circle

>> No.7060025

>>7060021
I cant speak russian or programming dude, post it in normal english please

>> No.7060027

>>7060024
It does if you do it to INFINITY

Infinity is a scientific fact, a measurement you can use


If you would do the squares untill INFINITY, you would actually reach 4


Of course, you would never grow old enough to do it but theoretically i mean..

>> No.7060028

>>7060027
because if you do it till infinity, the squares would become so small, almost 1 atom small, or 1 electron, which is basicly a circle. It just takes an infinite ammount of times to make it perfectly smooth


But still, theoretical, this makes it 4 right?


I do not understand how it would be 3 and not 4

>> No.7060029

>>7060024
But a circle is nothing else than atoms lining up which makes it seem round


There is no way it can be 100% round


There will always be if you use a microscope some dots, like pixals on your monitor or tv. From far away it looks round, but if you go closer, you see the pixels.


Same goes for a circle. Unless someone invents a perfect round circle, but still then how cant it be 4?


This is fucking breaking my brain

>> No.7060034

>>7060025
click the link instead of just floating the cursor and jsmath will activate

>> No.7060035

Can we get this to autopost or put it in the sticky or something

>> No.7060036

>>7060016
That website is wrong. Does that guy know the definition of a limit of a sequence? The limit need not be an element of the sequence, but we must be able to get arbitrarily close to the limit with members of the sequence.

>> No.7060039

>>7060035
>>7060016
Talking about this site

>> No.7060041

>>7060022

This guy is right. 4 is the theoretical measurement. 3.41 is what we use because circles can't exist in reality, only in pixels.

>> No.7060042

>>7060039
The website is wrong. That shape is not a circle, although it definitely looks like one. This shape is continuous but nowhere differentiable. A circle is.
>Here's the breakdown, as simple as I can make it
I get the feeling that this site is trolling too

>> No.7060051

>>7060036
Hmmm you need to define the curves as objects in a metric space to define convergence really which the article does not do.

A way to do this is: parametrise each curve by angle. Now each curve is an element in the space X of continuous functions from [0,2*pi] to R^2. A metric on this space, d_X, can be defined by if g and f are 2 elements in X, and d is the standard euclidean metric on R^2, then d_X(g,f)=sup{d(g(x),f(x))|x in [0,2*pi]}. This would be the standard way to do things.

Now it is clear that the sequence of curves DOES converge to a circle. There is a length functional L:X->R (really here you'd have to restrict the space X a little I believe to say piecewise differentiable curves or something). The issue with the pic in OP is it assumes, incorrectly, that this functional is continuous and therefore that if x_n is a sequence in X then limit L(x_n)=L(limit x_n).

>> No.7060057

I guess I have to be the one to tell you guys that inverting the corners to the limit of infinity will just make a infinitely rough jagged circular curve that will have a length of 4 not pi.

>> No.7060058

>>7060041

I hope you're trolling.

>> No.7060066

>>7060057

Nope. That limit will make a real, perfectly smooth circle. Its circumference, though, will be pi.

>> No.7060082

No matter how many corners you remove you will never have a circle just like how 0.999... will always be less than 1 no matter how many nines you have.

>> No.7060085
File: 113 KB, 953x613, .999...cequals 1.jpg [View same] [iqdb] [saucenao] [google]
7060085

how the fuck can .9999 be equal to 1 though
the numbers don't even look the same, it's like saying a circle is the same as a square
like what the fuck

>> No.7060086

>>7060082
The bait is strong with this one

>> No.7060088

>>7060085
Well if there's infinite nines, then no number can exist between .999.. and 1 so they are by definition the same

>> No.7060090
File: 649 KB, 1212x1044, banana..jpg [View same] [iqdb] [saucenao] [google]
7060090

>>7060088
>by definition
what if that definition is wrong in the first place

>> No.7060106

>>7060090
nobel underway

>> No.7060128
File: 5 KB, 355x323, stupid.png [View same] [iqdb] [saucenao] [google]
7060128

>>7060014
and the diagonal of a square is 2a, you got it right. I've just shown that to my maths professor and we'll be releasing new textbooks soon.

>> No.7060205

>>7060014
how do you get 4! from a perimeter of 4

>> No.7060207

>>7060014
where did the factorial come from?

>> No.7060470

>>7060014
Try walking across the diagonal points of a 100 m^2 square by two methods:

>Diagonal
>Crossing two sides

The cutting does not give the perimeter of S_1's boundary because the construction isn't smooth, whereas it can be proven (analysis) that S_1 has a smooth boundary.

>> No.7060485

This thread alone has made me realise there's as many shit posters on /sci/ as on /b/

>> No.7060489

>>7060014
It's like taking the area under a parabola using several trapezoids instead of Riemann sums. Its close but that little bit it's off is enough. Rounding the edges takes it from 4 down to the 3.14

>> No.7060505

>>7060019
>>7060014
It has to do with the definitions of a circle and a perimeter.

You could define "perimeter" differently so that pi would come out to 4, but it wouldn't be as useful a concept.

In the same way, you could define the length of a diagonal line such that the length of a hypotenuse of a right-angle triangle, with its legs aligned to the reference grid, as equal to the sum of the lengths of its legs, rather than the square root of the sum of the squares of the lengths of its legs, by conceptualizing diagonal lines as infinitely fine staircases, as curves are conceptualized in the original image.

If you conceptualize curves or diagonal lines as infinitely fine staircases, then your model become anisotropic: it matters what angles things are at. A line that is diagonal to the reference grid would be longer than one that is aligned to it. The model is unhelpful to determine the amount of time it would take you to walk a straight line between arbitrary points, or the minimum amount of material to build an effective fence along that line.

Our phrase "straight line" comes from the same roots as "stretched linen", or in other words, a tight string. As you turn a tight string through a reference grid, you don't get more or less string. This is a model of distance which is useful in the real world. Similarly, if you pull a string around the curve of a cylinder, you don't measure the details of any "infinitely fine staircase", even though the actual surface of a real-world object made of atoms is complex and rough.

>> No.7060700
File: 40 KB, 1347x308, ek is too dumb for calculus.png [View same] [iqdb] [saucenao] [google]
7060700

>> No.7060731

the answer is:

negative numbers fail in geometry

you can ADD to a shape
you can only add.

>> No.7061139

>>7060014
what if the radius is 0.5 instead of 1, does that makes a new Pi number that you can use in real life?

>> No.7061182

It's essentially a statement about convergence of integrals. The arc-length of a circle is given by an integral involving a function f. The arc length of any of the piecewise linear approximations is given by an integral involving some sequence of functions g_n, where as n goes to infinity we better and better approximate f. Then the problem is that while lim g_n = f pointwise, but NOT uniformly, so we can't apply a theorem to state that the limit of the integrals involving g_n equals the limit of the integral involving f.

>> No.7061186

https://www.youtube.com/watch?v=D2xYjiL8yyE

>> No.7061195

>>7060014
3/10 for getting me to reply, OP.

Now go back to /b/ if you want to make shitty troll posts.

>> No.7061250

does no one on this board have high school level education? The number of edges increases while the length decreases, but at the same rate so the overall length stays the same.

>> No.7061295

>>7060029
A perfect cicrcal is sonething that only exists as idea

>> No.7061380

>>7061250
That's not the point here. Not at all.

>>7061182
Explained it well. It's a problem of non uniform convergence or, if you prefer, a problem of non switching of integral and limit.

>> No.7061383

>>7061380
Wrong, it does converge uniformly. The absence of uniform convergence has nothing to do with the exchangeability of operations.

>> No.7061390

>>7060014
pi isn't a theoretical number

>> No.7062062

>>7061383
if you look at the formula for arclenght given as integral you see that you need uniform convergence of the derivative which obviously is not given

>> No.7062069

>>7060028
>because if you do it till infinity, the squares would become so small, almost 1 atom small, or 1 electron, which is basicly a circle.
stop posting please

>> No.7062347

You can't approximate a diagonal line through a quadricular line. The pythagoras theorem holds even for a triangle with infinitesimal sides. You can approximate a circle with a bunch of diagonal lines because if the infinite limit, the "effect of the curve" is a double infinitesimal, ignorable when added to a first order infinitesimal. That's also the reason why you can calculate an integral with rectangles.

>> No.7063292

>>7060205
you're a cheeky little one.

>> No.7063296

>>7060019
>>7060022
How can you only know pi to one digit?

>> No.7063301

>>7060014
https://www.khanacademy.org/math/recreational-math/vi-hart/pi-tau/v/rhapsody-on-the-proof-of-pi-4

>> No.7063319

>>7061295
...and as a band.

...and as a song by that band.

>> No.7063362

>>7063301

i like her videos, but she talks very fast and thinks she is so smart and artistic. that makes me want to kill her

>> No.7063364

>>7062347
very good indeed

>> No.7063673

>>7063362
I agree. She talks way too fast.

>> No.7063676

>>7061295
Is spelled "perfect circle", jerk.

>> No.7063731

>>7060024
this is right. that's not a circle op, that is a polygon with sides approaching infinity, all angles normal. if it was a polygon with sides approaching infinity and all sides approaching parallel to all other sides, then it would be a circle. and the perimeter would be pi. learn some analysis, op.

>> No.7063734

>>7063676
well, this is a perfect circle jerk

>> No.7063899

Why are there so many people in this thread thinking that pi is 3.41 and not 3.14? Did you not go to high school?

>> No.7063900

>>7063899
>Why doesn't everone rote memorize everything without comprehension?
Engineer detected.

>> No.7063911

>>7063899
i dont know whether to laugh at you or cry

>> No.7063913

>>7060085

>a simple proof by induction

stopped reading there

"proof" lol, absolute psudomath

>> No.7064414

>>7063899
8.60% error