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/sci/ - Science & Math


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File: 12 KB, 1217x376, sides.png [View same] [iqdb] [saucenao] [google]
6104468 No.6104468 [Reply] [Original]

Discuss

>> No.6104473

yes.
Although the perimeter doesn't necessarily converge to one of a circle.

>> No.6104477

>>6104468
There can't actually be infinite sides, so no
But certainly adding sides brings you closer to a circle

>> No.6104491

>>6104473
Yes it does, for a n-sided polygon, perimeter is <span class="math">2nRsin(\pi/n)[/spoiler].
sin(x)=x, as x->0, so as n gets large you get:
<span class="math">2nR\pi/n=2R\pi[/spoiler]

Same goes for area using <span class="math">A=0.5nr^2sin(2\pi/n)[/spoiler]

>> No.6104567

>>6104468

That's only one side, not infinite.

>> No.6104582

>>6104567
That's two sides. The inside and the outside.

>> No.6104583

>>6104582
also, the circle has a left and a right side.

>> No.6104586

>>6104473
>1989
>being this retarded

>> No.6104650
File: 48 KB, 350x494, piequals4[1].png [View same] [iqdb] [saucenao] [google]
6104650

>>6104491
>>6104586
>not necessarily
you'd expect educated people to know how o read

>> No.6104656

>>6104650
learn some analysis faggot

the shape in your pic does indeed converge to a circle

however S_n -> S does not imply P(S_n) -> P(S)

where each S_n is the set of points of each polygon, and S the set of points of the circle, and P the perimeter function.

>> No.6104660

>>6104656
thanks for making the exact point I was trying to make in this post >>6104473

Assburger much?

>> No.6104683

>>6104660
As I understand OP's pic, in that case it precisely does converge to 2 pi r, so your point is irrelevant.

>aspergers
>not in DSM-5
>so last century

>> No.6104714

>>6104656
>>6104650

This doesn't converge to a circle, but a diamond.

>> No.6104745

>>6104650
I'd like to see an L-system that does that

>> No.6104784

>>6104650
>draw a right triangle
>draw a rectangle around it, semiperimeter = sum of catets
>remove corners, semiperimeter still = sum of catets
>repeat to infinity, hypotenuse = sum of catets
>problem Pythagoras?