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/sci/ - Science & Math

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File: 8 KB, 470x222, RegularPolygons_800[1].gif [View same] [iqdb] [saucenao] [google]
6882380 No.6882380 [Reply] [Original]

The more sides a regular polygon has, the more it resembles a circle. Does this mean that a circle is a regular polygon with an infinite number of sides?

>> No.6882386

>>6882380

yes, that's how archimedes approximated pi.

>> No.6882388

>>6882380
>is
That's kind of a tricky word in mathematics. You can say that one thing "is" another thing, but it doesn't mean a whole lot, especially when talking about limits.

It would be more meaningful to say that regular polygons "approach" a circle as the number of sides "approaches" infinity.

>> No.6882396
File: 48 KB, 350x494, piequals4.png [View same] [iqdb] [saucenao] [google]
6882396

in general, you must watch out with such constructions. E.g. the points in pic related converge closed to the circle given by x^2+y^2=1, but the length of the line segments stays invariant at 4.

>> No.6882397

>>6882388
This
A circle has sides equal to 1/infinity or 1 point on a plane
The number of sides goes towards infinity

>> No.6882465

>>6882388
>You can say that one thing "is" another thing, but it doesn't mean a whole lot, especially when talking about limits.
I bet you argue that <span class="math">0.99\ldots\neq 1[/spoiler].

>> No.6882487

>>6882465
ha
how much, exactly, do you bet?

>> No.6882498

>>6882487
>how much, exactly, do you bet?
I have never heard someone say this line who isn't autistic.

>> No.6882514

>>6882498
I've never heard anyone use "autistic" as an insult on an image board who wasn't... well, you know how you are

>> No.6882526

>>6882514
>>6882498

autismintsifies.jpg
coffeemug.jpg
toolazytofindpics,soifakeimagefiles.jpg

captcha: reckless student
>am a student putting off studying and instead wasting time on 4chan

>> No.6882529

A circle is the collection of all points with the same distance to a point (the centre, obv.)

>> No.6882550

>>6882396
Is this because the length function is not continuous in Lp spaces?

>> No.6882556

>>6882498
He made you look retarded and I laughed. Now you're just acting like a pathetic kid.

>> No.6882607

>>6882550
Exactly. Polygons with many edges approach the circle in L^2_1, where length is continuous