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/sci/ - Science & Math

File: 223 KB, 710x810, FB_IMG_15715241020991471.jpg [View same] [iqdb] [saucenao] [google]

Anonymous Sat Oct 19 18:30:38 2019 No.11074783 [Reply] [Original]

Why /sci/?

>>	Anonymous Sat Oct 19 18:39:58 2019 No.11074801 >>11074783 Because the black outline is and never will be an actual circle

>>	Anonymous Sat Oct 19 18:40:58 2019 No.11074804 >>11074801 *is not

>>	Anonymous Sat Oct 19 18:41:29 2019 No.11074807 >>11074783 because distance =/= length

>>	Anonymous Sat Oct 19 18:42:33 2019 No.11074810 >>11074801 >>11074804 >inf is just a bigly number hurr durr

>>	Anonymous Sat Oct 19 18:43:01 2019 No.11074813 File: 8 KB, 713x492, lebesgue.png [View same] [iqdb] [saucenao] [google] >>11074783 You can prove literally any curve has any length larger than its own with that trick, lad.

>>	Anonymous Sat Oct 19 18:48:03 2019 No.11074828 >>11074813 Yeah to do length limits you need tangent lines

>>	Anonymous Sat Oct 19 18:50:22 2019 No.11074833 >>11074783 You found an UPPER bound for the value of Pi, you did not find the value of Pi.

>>	Anonymous Sat Oct 19 18:50:42 2019 No.11074835 >>11074783 Duplicate thread

>>	Anonymous Sat Oct 19 18:56:16 2019 No.11074848 >>11074783 /sci/ if you take the limit of this sequence, shouldn't it be equal to pi? If not, why?

Anonymous Sat Oct 19 19:04:00 2019 No.11074864

>>11074848
>if not, why
You can approximate the length of the circle from the inside (by marking points along the circle and tracing lines from one to the next) because of Euclid's axiom that a line is the smallest path between any two points.
You can also approximate it from the outside, by tangent lines, because of the metric tensor, but that one's harder to explain.
Any third approximation is only correct if it coincides with these two.

>>	Anonymous Sat Oct 19 19:11:33 2019 No.11074880 >>11074833 based as fuck

>>	El Arcón Sat Oct 19 19:14:15 2019 No.11074889 After you repeat to infinity, there is an infinite number of corners. Circles have zero corners and zero is not equal to infinity.

Anonymous Sat Oct 19 19:22:33 2019 No.11074917

>>11074813
This
A line is 1 dimensional, to try to express it as a limit of a 2 dimensional object doesn't work.
You would have infinite corners, and corners aren't a property of a 1-dimensional object
It would be the as me trying to express the area of a plane using the surface of pyramid, you can't get entirely rid of the extra dimension

>>	Anonymous Sat Oct 19 19:36:57 2019 No.11074963 It doesn't approach the circle's circumference. It will always have a perimeter of 4.

Anonymous Sat Oct 19 19:51:11 2019 No.11074996

>>11074783
Through this process you find a line which is arbitrarily close to the circle, but it doesn't converge again the circle. Note that to say "converge against" you need a notion of metric/topology, and your construction never goes towards any smooth curve.

Anonymous Sat Oct 19 20:45:41 2019 No.11075129
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>>11074801
Infinity is not a big number you fucking underage high schooler.

>>11074807
But it is equal you stupid sophomore.

>>11074833
Try again, freshman.

>>11074848
Arclength is not continuous for the uniform norm.

>>11074889
Stupidest comment of the day. Definitely 11th grade and underage.

>>11074996
Most tryhard pathetic answer. Probably freshman trying to sound smart. Failed miserably anyway.

>>	Anonymous Sun Oct 20 02:24:24 2019 No.11075793 File: 45 KB, 512x512, lAxMD4d1.jpg [View same] [iqdb] [saucenao] [google] Oh look it's this thread again.

>>	Anonymous Sun Oct 20 03:11:54 2019 No.11075856 >>11074783 hurrays door I don't understand infinity

>>	Anonymous Sun Oct 20 03:14:17 2019 No.11075858 >>11075129 Can you explain it then?

>>	Anonymous Sun Oct 20 07:26:33 2019 No.11076344 >>11074917 /thread

>>	Anonymous Sun Oct 20 09:03:24 2019 No.11076508 >>11074783 circles do not exist and are infact just bent lines brainlet

>>	Anonymous Sun Oct 20 09:18:08 2019 No.11076530 you can say that it tends to 4, but it's not really 4

>>	Anonymous Sun Oct 20 09:30:14 2019 No.11076552 >>11074810 It is.

>>	Anonymous Sun Oct 20 09:32:18 2019 No.11076554 >>11074917 based, this explanation makes so much sense

Anonymous Sun Oct 20 10:11:02 2019 No.11076652
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I made a version of this meme earlier with an explanation. It all comes down to how you want to define length. With a taxicab metric d(a,b) = |a_x - b_x| + |a_y - b_y|, the perimeter of an euclidean circle would indeed be 8.

Anonymous Sun Oct 20 10:15:51 2019 No.11076665

>>11074917
> to try to express it as a limit of a 2 dimensional object doesn't work.
A square is also a 1d object, as well as are polygons that are not filled in.
>You would have infinite corners, and corners aren't a property of a 1-dimensional object
Literally the same thing can be said about the ACTUAL definition of the length of a differentiable curve - you approximate the curve with polygons and take the limit as the number of corners goes to infinity. Also you seem to be fundamentally confused about what infinity is, there's no actual shape at the end of the process in OPs pic, it's just a sequence of shapes. The endshape is undefined, so it doesn't make sense to talk about it. All limits are inherently defined in finitistic terms, which includes the length of an arbitrary curve.
You have no idea what you're talking about and the people who replied to you with "/thread" should be embarrassed.

>>	Anonymous Sun Oct 20 10:23:41 2019 No.11076692 File: 3 KB, 635x223, r8.png [View same] [iqdb] [saucenao] [google] >>11076552 inf is larger than any number. think. inf can't be a number.

>>	Anonymous Sun Oct 20 10:24:34 2019 No.11076696 Optical illusion

Anonymous Sun Oct 20 12:58:55 2019 No.11077046 [DELETED]

>>11076665
>You have no idea what you're talking about and the people who replied to you with "/thread" should be embarrassed.

Not the guy who said "/thread" but why should he?
I don't have a fucking clue of why the pic in op is wrong, and his explanation seem to make sense (before yours at least).

>>	Anonymous Sun Oct 20 14:51:20 2019 No.11077390 >>11074783 I hate irrational numbers. Pi should be 4.

>>	Anonymous Sun Oct 20 14:54:40 2019 No.11077405 >>11075129 >Stupidest comment of the day. Definitely 11th grade and underage. You're about to get us buried in timesand anon, plz stop

>>	Anonymous Sun Oct 20 15:51:02 2019 No.11077556 >>11074783 Here it is explained in laymanistic terms by no other that the odd1out https://youtu.be/kTVRopTVjpQ

>>	Anonymous Sun Oct 20 17:13:45 2019 No.11077766 Pointwise convergence of the jagged parametrisation to the circle does not mean we are able to interchange limits and integrals (the integral is the arc length).

>>	Anonymous Sun Oct 20 17:25:21 2019 No.11077795 It is only pointwise convergent, not uniformly convergent.

>>	Anonymous Sun Oct 20 18:31:46 2019 No.11077948 You could do the same drawing of a divided up square inside the circle and end up with pi = 2\sqrt{2} or something.

Anonymous Sun Oct 20 18:37:54 2019 No.11077961
File: 333 KB, 1271x1248, __flandre_scarlet_and_remilia_scarlet_touhou_drawn_by_rei_tiny8ao3m45elwl__20963417153f22304c8d22369d9a1519.jpg [View same] [iqdb] [saucenao] [google]

>>11077795
>it's only pointwise convergent, not uniformly convergent
No, the curve definitely converges uniformly to the circle.
Unless you mean something else converges pointwise?
>>11077948
No, you couldn't.

>>	Anonymous Sun Oct 20 19:03:28 2019 No.11078020 >>11076692 if it isnt a number, then you cant use it to prove that one number (4) equals another number (pi)

Anonymous Mon Oct 21 01:42:41 2019 No.11079032

>>11078020
The math is crude compared to normal numbers, like using a sledge hammer instead of tweezers.
So with a lot of operations it isn't clear how it should go.
But a mere real number being cut up by infinity - the numerator gets totally eliminated.
There is no problem of infinity being held back in any way.

>to prove that
it doesn't. Nothing is shrinking in the setup so it's a lame duck to begin with, all it does is give an upper limit of what pi can be.
pi < 4

Anonymous Mon Oct 21 10:14:17 2019 No.11079760 [DELETED]

>>11074917
Now that I think about it you could theoritically do the same with a pyramide and a square.
If you flatten a pyramide to a square an infinite number of time it should have the same surface perimeter as the square, wich obviously doesn't make much sense either.

>>	Anonymous Mon Oct 21 10:29:05 2019 No.11079796 >>11077961 >No, the curve definitely converges uniformly to the circle. That's not a thing. Functions can converge uniformly to something, not curves.

>>	Anonymous Mon Oct 21 10:30:08 2019 No.11079800 Pi = infinum of area of all polygons which contain the unit circle. Ergo, pi = 3.14.... QED

>>	Anonymous Mon Oct 21 10:57:28 2019 No.11079849 >>11079796 it's easy to parametrize the curves such that they converge uniformly to the circle (parametrized the standard way as (cost,sint)). uniform/pointwise convergence is not the issue here.

Anonymous Mon Oct 21 15:35:38 2019 No.11080284

>>11074917
>A line is 1 dimensional, to try to express it as a limit of a 2 dimensional object doesn't work.
you're wrong and that's not what's happening. the picture shows a sequence of curves converging to another curve.

>>11074996
>Through this process you find a line which is arbitrarily close to the circle, but it doesn't converge again the circle.
it does. undergrad detected.

>>	Anonymous Mon Oct 21 15:58:11 2019 No.11080331 >>11080284 You're being too harsh on undergrads. I'm a sophomore and I understand perfectly well what's going on. OP's pic shows that with the taxicab metric, the circumference of the euclidean circle with diameter 1 is indeed 4.

>>	Anonymous Mon Oct 21 16:02:51 2019 No.11080339 >>11080331 can you define circumference of the euclidean circle in the texicab metric ?

>>	Anonymous Mon Oct 21 16:07:59 2019 No.11080348 >>11080339 of course. You define it the same way as you do with euclidean metric. Supremum of (sum d(x_i, x_(i-1)) where x_i = f(t_i) are points along the curve such that 0=t_0 < t_1 <... < t_n = 1.

>>	Anonymous Tue Oct 22 05:32:04 2019 No.11081920 >>11075858 Read again.

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