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/sci/ - Science & Math

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6244165 No.6244165[DELETED]  [Reply] [Original]

>> No.6244342

>>6244165
if you do the same for a triangle it will show that the hypothenuse = adjacent side + opposite side. which is obviously wrong and shows that the here applied method is flawed.

>> No.6244451

>>6244165
take a piece of paper that is 4 units wide. form it into a circle with the edges of the paper touching but not overlapping. measure the diameter. I get ~1.25 since this does not fit your theoretical answer then your theory must be wrong.

>> No.6245101

>>6244342
>>6244451
>hurr I was only pretending

>> No.6245140

will someone explain the flaw in this method please

>> No.6245150

>>6245140
The result from this method isn't a circle, you get a diamond shape, or rhombus, or whatever the fuck you want to call it.

>> No.6245163

>>6245150
oh yes i see. thank you anon

>> No.6245166

This thread is full of trolls.

>> No.6245468

>>6245140
No flaw, only the conclusion is wrong, all that this proves is that <span class="math">\pi \leq 4[/spoiler]

>> No.6245476

>>6245150
BS. The result is a circle with a circumference of 4. This however is not the same as the circumference of the blue circle. Infinity is tricky and can create weird effects like this, another famous example where infinity causes totally unintuitive effects is the doubling of a ball surface area: http://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox

>> No.6245490

>>6245476
>BS. The result is a circle with a circumference of 4.
Circles don't have squared sides, and you are only eve producing a shape with squared sides. It is not a circle.

>> No.6245491

the edges on the corners are infinitesimal 90 deg angles which make the "circle" have 4 perimeter.
Its a nice example why math is a failure with respect to infinitesimals. The circle is just like the difference of 1-0.999... amplified to infinity(infinitesimals) giving extra(4-pi)perimeter demonstrating you can't ignore infinitesimals.
>mfw when everyone believes that 1=0.999...

>> No.6245493

>>6245491
>why math is a failure
You not understanding it doesn't make it a failure, anon.

>> No.6245494

>>6245493
I understand the problem perfectly.
The edges at infinity are equal to a circle in standard math. In intuitive math they don't disappear just like the difference with 1-0.999... doesn't disappear . the circle problem amplified the "infinitesimal" difference between the true circle(0.999...) and the fake circle(1) into a tangible difference between pi and 4.

>> No.6245496

>>6245490
It's a perfect circle, anything less that that means we're not talking about infinity, just a durr huurr biggg numbah

>> No.6245498

>>6244165
>mfw mathfags are forced to admit that either infinitesimals exists(1>0.999...) or that pi=4(retarded)

>> No.6245501

>>6245498
mathfags admit that <span class="math"> \pi \leq 4 [/spoiler]

>> No.6245502

>>6245501
If the circles are equal pi is exactly 4. Since infinitesimal corners don't exist pi=4

>> No.6245506

>>6245502
The circles aren't equal. The blue's circumference is pi and the other's circumference is 4. They are not the same.

>> No.6245513

>>6245506
Then infinitesimal corners exist and 1>0.999...

>> No.6245519

This process will yield a concave polygon very similar to a circle, but with countably infinitely many faces. A circle contains uncountably infinitely many points. Therefore, even continuing this process to infinity, the outer polygon will never actually become a circle.

>> No.6245521

>>6245513
Nope, the processes are different.
0.999... is constantly creeping towards one and if it goes on for infinity, it reaches it.
The black line on the other hand isn't shrinking at all, there is no shrinking process going on. At all times its length stays at a constant 4.

>> No.6245522

>>6244165
>muh x, y axis

>> No.6245524

>>6245519
>countably infinitely
lel

>> No.6245526

>>6245521
The outer circle converges to exact same shape as perfect circle.
0.999... Converges to 1 with every extra nine.

>> No.6245529

>>6245526
Not all math can be drawn. 5-dimensional cubes for example. Doesn't make them impossible in math. Pictures are just cute hand-wavy approximations, analytical results rule.

>> No.6245532

>>6245526
>same shape
Exactly. Shape - but not length

>> No.6245533

>>6245524
Yes, countably infinitely many. I'm not certain, but I think that for the nth step, we have the number of faces equal to <span class="math">4(2^{n+1}-1)[/spoiler]. It's pretty clear that we can create a bijection between this and the natural numbers, i.e. the number of faces will be countably infinite.

>> No.6245537

>>6245533
Listable is a better word. All that means is that you have a way of getting to an arbitary number by moving along a list of some kind. What it doesn't mean is that you can reach infinity.
See http://www.youtube.com/watch?v=elvOZm0d4H0 at about 2:00

>> No.6245539

>>6245537
I am a fan of Numberphile, but keep in mind its target audience is the general public. "Countably infinite" has a specific meaning in mathematics, a good overview of which is here: http://mathworld.wolfram.com/CountablyInfinite.html

>> No.6246496

Pi does not equal 24.

>> No.6246600

Let S_n, n = 1,2,3... be the shapes generated by this process. That is, S_1 is the cube and so forth. Let C : {S_n} -> R be the function that calculates the circumference of the shapes.

Obviously, lim S_n is the circle. But we do not know that C(lim S_n) = lim C(S_n) (it obviously isn't, in fact), so we cannot conclude that pi = 4.

>> No.6246612

>>6246600
>Obviously, lim S_n is the circle

Well, ok, it depends on what norm you choose to measure distance in the normed space containing these shapes, so maybe it isn't obvious. Regardless, the following statement holds.

>> No.6246702

Niggers can't understand convergence

>> No.6246741

>>6245496
Fractals

>> No.6246764

>>6244165
4 factorial ?

>> No.6246777
File: 126 KB, 600x500, 1387938684177.png [View same] [iqdb] [saucenao] [google]
6246777

>>6245476

That actually isn't a result of infinity. It only takes 5 pieces.

>> No.6246812

>>6246777
Your example picture only shows 4 though.

>> No.6247090

I think this problem it too simple, set the whole thing spinning so that Lorentz contraction will shorten the circumference but not the radius and you finally get something interesting.
http://simple.wikipedia.org/wiki/Rigidly_rotating_disk_paradox

>> No.6247097

Infinty, circles etc only exist for math.It doesnt apply for our universe.

>> No.6247098 [DELETED] 

>>6246812
5, one of them has to be arrow-shaped of it doesn't work.

>> No.6247102

>>6246812
5, one of them has to be arrow-shaped or it doesn't work.

>> No.6248277

Did OP disproved math?

>> No.6248304

>>6244451
>theoretical answer
Lol wot. Maths in a pure form has nothing to do with tangible objects. Go back to engineering.

>Apply similar method to hypersphere in 76 dimensions
>Get similarly wrong answer
>Disprove with paper plz

>> No.6248335

>>6244165
Congratulations, you just discovered fractals

>> No.6248389

>>6248304
I would agree with you in the context that this were about abstract geometry, but the OP is clearly about a circle drawn on a piece of paper. Hence 'draw a circle' 'remove corners' etc.

>> No.6248558

>>6248335
There is no fractal. The corners sides are length 0 at infinity.

>> No.6248571

The integral diverges. At any finite point you'd still have the same square perimeter only at infinity are they exactly the same. They go by Lesbugue integrals if I'm not mistaken.

>> No.6248663

Lrn2triangle-inequality, Pleb

>> No.6249912

>>6248663
It's a circle and not a triangle.

>> No.6250161

>>6245468
Wrong, proves that π < 2

>> No.6250174
File: 11 KB, 216x108, 1388113463644.png [View same] [iqdb] [saucenao] [google]
6250174

>>6249912
Each circular arc <span class="math">c_n[/spoiler] is associated with a vertical line segment <span class="math">a_n[/spoiler] and a horizontal line segment <span class="math">b_n[/spoiler] which together approximate a right triangle, the approximation becoming better as more corners are removed. By the triangle inequality, <span class="math">c_n < a_n + b_n[/spoiler] therefore π<4