/sci/ - Science & Math

[Anonymous No.11962401]

/sci/ btfo'd

[Anonymous No.11962410]

I wonder how many people on this board won't realize that there are now infinite triangles with a non-zero area that add up to exactly 4 - pi units.

[Anonymous No.11962419]

Pro tip: the unit circle arc length is 2*pi

[Anonymous No.11962420]

If this was known from antiquity, why it took so long for fractals to be a thing?

[Anonymous No.11962421]

>>11962401
>repeat to infinity
and therein lies the problem

[Anonymous No.11962423]

>>11962401
>>11962421
What’s the actual answer? Also, I’m almost certain the first time I saw this was from ducking wilderberger or whatever his name is.

[Anonymous No.11962432]

>>11962423
It is. The issue is that you can never perform the infinite number of operations, so the whole premise is invalid.

[Anonymous No.11962434]

>>11962432
(You)

[Anonymous No.11962436]

>>11962434
(me)

[Anonymous No.11962475]

>>11962401
the limit of the sum of arc lengths is not the same as the sum of the limit of the arc length.
next question

[Anonymous No.11962511]

>>11962401
this is indeed a proof that 4 is an upper bound of pi

[Anonymous No.11962535]

>>11962475
What does this mean? The way I understood it is even after infinitely many steps there’s still infinitely many more points outside the circle than on it, which obviously don’t have length 0. Can’t understand how to put that into math though.

[Anonymous No.11962604]

>>11962423
>actual answer
all it shows is that pi<4

[Anonymous No.11962615]

>>11962535
[math]\lim \sum ds \neq \sum \lim ds[/math]

[Anonymous No.11962639]

>>11962615
First would be equal to the circle right? I’m not sure where the second comes from. Wouldn’t [math] lim ds[/math] be equal to 0 or an infinitesimal?

[Anonymous No.11962670]

>>11962401
>repeat to infinity
you do realize if you actually do this then it stops being a circle and becomes a square and then the whole shenanigans starts over again otherwise it wouldn't be infinite

shapes are just a snapshot of the current timeline, they aren't time itself
just look at human history and their architecture
every timeline has distinct architecture

[Anonymous No.11962855]

>>11962436
"My cock is only measurable on the affine plane"

[Anonymous No.11962861]

>>11962670
>numbers
>timeline
what next, dressing little hats on them?

[Anonymous No.11962962]

the sequence of the square like curves definitely converges to the circle. but there's no mathematical principle which would imply that lengths of the curves must converge to the length of the circle. actually, this picture provides a counter example.

[Anonymous No.11962970]

>>11962401
scientists btfo sure
but mathematicians no. that's not mathematically the perimeter of a circle

[Anonymous No.11962972]

>>11962615
i smell that this is the wrong answer. am i right?

[Anonymous No.11963067]

>>11962972
no.

[Anonymous No.11963092]

>>11962423
>actual answer
I'm sure you already know that pi isn't 4, anon.

[Anonymous No.11963666]

>>11962401
>an accordion is only as long as the box it came in

[Anonymous No.11963740]

>>11962401
the error of the approximation must be a "higher order infinitesimal" than the infinitesimal approximation element itself. when you approximate the arcs with straight segments, the limit of ratio of the difference between arc length and segment length on one hand and segment length on the other hand is zero, so the diffference / error is a higher order infinitesimal than the element. here the same limit is non-zero, at any point you have a series of similar triangle-like constructs of decreasing size, and the difference between the sum of lengths of the two straight segments and the arc segment is an infinitesimal of the same order as the arc segment.

[Anonymous No.11963769]

>>11962423
the figure defined in OP is not a circle, since it's perimeter is not everywhere at a right-angle to a straight line subtended from the center of the figure to its edge (in fact is is only at a right-angle at 4 points)

[Anonymous No.11963822]

>>11962615
>>11962972
It’s wrong in general. It’s not necessarily the case that they’re not equal, they just don’t have to be. A proper explanation would show why they’re not in this case.

[Anonymous No.11963851]

>>11963740
>>11963769
Both of you are wrong. The limit of the process is indeed a true circle. The “troll” here is simply conflating two ideas. There’s no reason why the limiting object should have same perimeter as the perimeter of the process, as >>11962615
sort of said. Since they’re not necessarily equal and assuming they are leads to a contradiction, we can assume they’re not equal.

[Anonymous No.11963854]

>>11962410
Is it a triangle if the hypotenuse is curved?

[Anonymous No.11963872]

>>11962410
What part of that is meant to be surprising? The convergence of an infinite series is literally a calc 1 topic.
>>11963854
It’s not curved. You’re approximating arc length with line segments, the line segment being the hypotenuse. The limit of the approximations is the actual arc length.

[Anonymous No.11964519]

>>11963851
>Both of you are wrong
how am I wrong? (I'm >>11963740) I never said anything about the limit being or not being a circle, indeed I explained why the length is not converging to the true value. all you said was "sometimes it converges and sometimes it doesn't".

[Anonymous No.11965015]

>>11962420
Well a lot of knowledge was lost with the burning of the library of Alexandria. It's possible it was discovered but was disregarded as schizo shit. Nowadays they wouldn't be nearly as popular if it wasn't for some cool sounding names (i.e. fractal, chaos theory, etc) and the I FUCKING LOVE SCIENCE niggers, so yeah.

[Anonymous No.11967864]

>>11962432
>you can never perform the infinite number of operations
do know about power series ?

[Anonymous No.11967922]

>>11962670
based schizo.

[Anonymous No.11968064]

>it's another freshman thinks everything commutes episode

[Anonymous No.11968155]

>>11962401
You discovered an UPPER limit for PI is 4.
Good job!

[Anonymous No.11968568]

>>11965015
>byrning of alexandria