/sci/ - Science & Math

Pi is a Transcendental number. It Can't be squared using a finite number of steps

Even doing so ad infinitum will never produce a circle. The radius will always vary.

It's wrong because the area of an object has almost no relation to the length of its perimeter.

>>2169090
agreed

\thread

0.9 isn't 1.
0.99 isn't 1.
0.999 isn't 1.

repeat to infinity.

0.999... isn't 1.

That's it. Everyone who says this does NOT approach a circle is just as stupid as the fucktards who claim 0.99.. isn't 1.

Now fuck off.

>>2169096
The picture doesn't require area.
It just shows that the circumference of the circle = pi
Perimeter = 4

It's wrong because pi is a transcendental number and can't be generated that way.

>>2169103
what has pi being transcendental to do with this at all?
Of fucking course you can approximate transcendental numbers by an infinite iteration. What are you, 12?

PROTIP: this has absolutely nothing to do with pi being transcendental.

>>2169111
substitute approximate with "write [..] as"

That image implies any line tangent to a circle is perfectly horizontal or verticle, this obviously isn't true.

>>2169102
wrong. induction does not work with infinities.
the area approaches the area of the contained circle, but the perimeter remains constant

>>2169115
THANK YOU.
This can btw be illustrated in a way even the average sci-fucktard can understand it.

There's a variation of the troll in OP's picture which shows sqrt(2) = 2 using the very same method, and obviously sqrt(2) isn't transcendental.

inb4 >sqrt(2) is transcendental
hahaha, really, I wouldn't be surprised...

I don't get it. What argument is this picture even trying to make, besides an appeal to intuition?

OP: by using perpendicular lines you're approximating a shape while never altering the perimeter (taxicab geometry).

You can use similar falacy to "prove" that the length of a staircase with an infinite number of infinitesimal steps is 2, as opposed to 1.4 (root2). Pic related

>>2169129
It even works for natural numbers of you use a 3-4-5 triangle.

>>2169127
>i'm a retard
>please rape my face
If you have anything to contribute (you don't), please feel free to do so. (Not really though, because you have nothing to contribute. Shut the fuck up.)

OP here, while we have definitely established that this picture is wrong...i'm not exactly sure why still. You all seem to be in complete disagreement on how it's flawed..just that it is.

Or actually I think one person said it's not and then gave a reason someone else used to explain...why it is?

...I think I need to go back to college. WHY DID i MAJOR IN THE ARTS!?

Wait, if the circumference of the circle is 4, why would pi be equal to 4? The circumference is 2pi*r. The only thing you can conclude there is that the radius is 2/pi.

>>2169165
It's wrong because it shows (correctly) that you can construct something looking somewhat like a circle with a perimeter of 4, and then for no apparent reason (and wrongly) concludes that a circle also has a perimeter of 4. That step doesn't follow from the premises and is therefore wrong.

>>2169165
your answer is precisely here: >>2169102
Just because something holds for every step of the iteration (0.999..9 (finite number of 9s) isn't 1), doesn't mean it holds in the limit.

tl;dr: you're an idiot and don't understand limits. Take analysis 1 and come back. Before you do, fuck off.

>>2169174
for someone who claims to understand analysis, you sure don't know fuckall about convergent series

because a straight line between two points is not the same as a series of perpendicular lines between the same two points.
/fucking thread

>>2169174
>HUR DUR YOUR STUPID BECAUSE IM SMATER

>>2169190
what are you talking about? Have you even read my posts?
0.9 isn't 1
0.99 isn't 1
AND SO ON.

If you repeat adding 9s to infinity, the picture in the OP might argue that 0.999... isn't 1, since that was how it was in every step of the iteration.

But that's retarded, like I said before.. Fucking idiot. Perhaps read the posts you're responding to.

>>2169207
>your opinion>my opinion

>>2169180
if the square at the beginning has perimeter 4, then the circle has diameter 1 and thus circumference pi..

>>2169196
>HURR IM STUPID CUZ IM 12

Haven't any of you ever worked with Koch's snowflake? That's a clear example of how infinitely iterated fractals don't behave as we might expect.

ITT:
>sage, sage everywhere

>>2169165
Dear OP: if you construct a shape out of nothing but horizontal and vertical lines (like in your circle example) then it'll only be an approximation for all parts of the circle that aren't exactly horizontal or vertical. Also in the staircase example, the two perpendicular lines have a longer combined length than the diagonal line (hypotenuse) they're approximating.

Long story short, no matter how many steps you take, your shape will always only be approximating a true, mathematical circle.

>>2169207
Speak clearly you faggot.
Are you saying that it is a circle, and it has circumference of 4 or not?

>>2169228
the iteration converges to a circle, so yes, "after" infinitely many steps that iteration would yield a circle.
inb4 >hurf infinitesimally small right angles
anyone who doesn't agree that this approaches a circle simply doesn't understand limits at all.
If you're going to argue with infinitely small quanteties, you might as well argue that 0.999.. isn't 1, since it's "infinitesimally smaller than 1" (yes, that is motherfucking fucktarded, but you'll probably make the very same argument because you can't accept the iteration approaching a circle, because you don't understand what "approach" means in this context).

And obviously the limit, being a circle and all, does NOT have perimeter 4, fucktard.

ITT: niggers doing science

>>2169222
Only that it's not a fucking fractal. Idiot.

>>2169227
no matter how many 9s you add, 0.999...9 (finitely many 9s) will NEVER yield 1, it will always only be approximating the mathematical true 1.

(I hope you see your own retardation by now. If not:
the LIMIT of adding 9s obviously is 1, just as the limit of the iteration is more or less obviously (for idiots at least) a circle. That's what limits are about.)

Infinitely many steps is impossible OP.
It's like division by zero.
How many zeros does it take to make one? No matter how many you have, even if it's infinite it'll never progress.
The same could be said with OP picture. By definition, it will never be a true circle. A circle is a line of infinitely many points that encompass a single point in the center, each exactly the same distance from that point.

Since OP's picture parameter is 4, somewhere along the lines- the points' distance from the center changes. It must be exactly the same.

You can 'refine' it as much as you like, but the parameter MUST be pi to for it to be a circle. OP's picture is merely a refined polygon.

>>2169283
>Infinitely many steps is impossible OP.
Yes you fucking idiot. Surprise: in analysis you don't actually have to carry out infinitely many steps to be able to talk about limits.

Perhaps look up what a limit is before you participate in a discussion which is way out of your league.

Assumption: Infinite iterations of this kind perfectly produce a circle, the perimeter is conserved, even in the limit (any others?)
=> The ratio of the circumference and diameter of this "circle" is not pi
=> Contradiction

Shouldn't that mean that one of the assumptions is false? Actually, I'm really curious, has /sci/ put together a convincing explanation to this problem?

>>2169102

2 isn't one
Barack obama isn't 1

Therefore numbers don't exist whatsoever

>>2169299
No, they haven't.

read up on taxicab geometry op

Look the answer is simple, a perimeter cannot be judged on a system of reduction towards a finalized abstraction such as the implied curvature, right? So then the basic assumption that you can substitude an actual circle for one imagined in the complex plane (ala fractalss) is silly

It's because you're only using the set of the integers when pi lies in the set of the irrationals.

>>2169294

You're clearly out of your own league, son. Read the definition of what a circle is.

>a closed plane curve consisting of all points at a given distance from a point within it called the center

That picture doesn't have ALL the points, each with the EXACT same value. Even if it's off by just a bit, it's not a circle, and therefore any talk about its relation to pi is void.

>>2169207

2=/=1
1/2=/=1

therefore 1=/=1

Because the square can never be reduced to a perfect circle

>>2169103
Transcendental has nothing to do with it. An infinite number of operations can produce a transcendental number, but in this case the limit of the perimeters does no equal the perimeter of the limit. This is because "perimeter" is not a continuous function.

>>2169066
Continued to infinity on that pattern you will successfully produce a diamond

Wait i'm confused. If I square can never be a perfect circle just how the heck do you get a square by combining two triangles, those two clearly arent related.

Is a circle not a shape?

>>2169190
go back to algebra 2 man
converges =/= equals
think of 1 as an asymptote of .9999...9

>>2169327

>>2169410
no. when dealing with infinite sums, convergent exactly means equals.

>>2169409
It isn't a matter of related shapes, simply the fact that these are straight line segments at right angles trying to become a CURVE shows that it will never work

>>2169102
There you have it folks, 3 thirds is not equal to one as one third is equal to .333...

1/3 =/= .33333...3
that is an approximation

>>2169430
get out

>>2169449
That's not how ... works.

Can't we just get a sticky for this shit?

>>2169449
Jesus H. Christ

Oh /sci/ you so wacky.
Never change.

>>2169180

eighth grade maths GENIUS alert

>>2169409

what in the world of fucking fucks am i reading here

OP here, from what I can gather from this, the image is obviously wrong, but I'm still not getting WHY. You guys just keep arguing.

>>2169742

IT'S WRONG BECAUSE THE LIMIT OF SOMETHING (IN THIS CASE, THE SEQUENCE OF APPROXIMATIONS) AND THE ACTUAL SOMETHING (PI) ARE NOT ALWAYS EQUAL, AND THIS IS ONE DEMONSTRATION WHY.

AS ANOTHER EXAMPLE, SEE:

.9 != 1.
.99 != 1.
.999[...]9 != 1

THE APPROXIMATIONS WILL NEVER EQUAL ONE, EVEN IF (GRAPHICALLY) THEY WOULD APPEAR TO, WHILE THE ACTUAL VALUE .999[...] *DOES* EQUAL 1.

SEE THE PARALLEL?

It's not a question of limits. The zig-zaggy perimeter=4 shape does *not* approach the perimeter of the circle at all. It just never does.

As you reach the limit, the circle is smooth and has circumference pi, while the zig-zaggy shape is infinitely jagged and has perimiter 4.

Thanks for asking a question which isn't just lame high school homework though.

>>2169919
Holy fuck you know math AND traditional games? I like you.

>>2169987
NOT AS WELL AS I'D LIKE TO,
>>2169948
POINTED OUT ANOTHER WAY OF THINKING ABOUT IT.

>>2169948
It has everything to do with limits.

You are correct when you note that the length of the perimeter of the piecewise strait shapes does not approach the length of the circumference of the circle. However, the set of points bounded by the perimeter does approach the set of points bounded by the circle.

The whole point is that equality of one limit does not imply equality of the other.

So to people saying that right triangles taken infinitely can never make a curve...

What about the arc length formula in calculus? It is derived by essentially taking an infinite numbe of right triangles and using the pythagorean theorem as the arguement of your rieman sum.

If the arc length formula is to be believed (And based on the lack of people arguing that the perimeter of the circle isn't pi, I'm willing to assume we all do), then we must therefore accept its origin.....which means accepting that an infinite number of right triangles DO create a curve.