/sci/ - Science & Math

>curvatureofearth.jpg

A straight line is a circumference arc of infinite radius. whats the problem?

...that pic just blew my mind...

You mean a given segment would be a (almost) straight line. Otherwise it wouldn't be a circle.

also
>asyptote

>>3455606

>He doesn't understand infinite

Asymptote, bitch. Gtfo with your troll science.

>>3455606
>I don't understand infinity.

Relax, we're here for you.

>relativity

universe is expanding at speeds fater than light, but you'll never see anything go faster than light

herpity derp

In conclusion, little girls actually have the biggest breasts of all. That's why they're so attractive.

>>3455631

LOLNO

>>3455634
never saw that picture huh?

someone post is please

>>3455668

lolohwait yeah I have.

It's obvious fallacious though.

define circle. directed to everyone

>>3455675

edit: obviously*

>>3455681

A circle is a simple shape of Euclidean geometry consisting of the set of points in a plane that are a given distance from a given point, the center.

A circle, by definition, cannot be infinitely large.

/thread

A. There are infinite dots on a circle.
B. Therefore there are infinite diameters (as in lines going from one dot to another through the center).
C. If you increase the distance of one dot (or several) from the center, thus making the diameters of these dots longer, the geometric shape is no longer a circle.
D. Thus we conclude you are wrong and a faggot.

>>3455696

I wonder, what is it like having an IQ of 100?

this
>>3455693
and this
>>3455696

/thread

>>3455696
I reject your definition.

Besides, we're talking about a limit here.

well there's the "circle at infinity" in projective geometry and it is infinite and treated as a line.

>>3455705
>implying all circles are the same size
What the hell, man? I'm thinking you just don't understand infinite sets.

>>3455705

>>3455668

I don't buy this "is a line" bullshit.
If you take the curvature at the bottom and at the right you get straight lines with different equations so it can't be a single line.

>>3455765

You must be a woman...

>>3455765
Limits and infinity. You don't understand them. It isn't a circle with a very large radius. It's the limit of a circle as radius goes to infinity.

>>3455765
What's your reference point when you say "bottom" and "right"?
The "infinitely far away" "center" of the circle?
How do you even know in which direction it is, judging from any point on the circle?

>>3455775

Limit of the curvature of a circle as the radius goes towards infinity, yes.. but what is the "limit of a circle"?

>>3455776
The line is perpendicular to the radius. Since the center is infinitely far away, all you can pick is the direction to the center, and that defines the "angle" of your line.

It's infinitely many straight lines, if that helps.

>>3455754

I understand now..

>>3455754
thanks

>tumblr_lmkzvviDGb1qanp23o1_500.png
4/10 would get trolled again

>>3455782
The limit of the circle when radius goes to infinity. You can't talk about limit of something when you don't say what is approaching what.

SURE IS PROJECTIVE GEOMETRY IN HERE

When you increase the diameter of a circle, the curvature decreases. so far, so true. But there really is no reason to assume that the limit of a sequence of circles is a circle. The limit of the circumference is a line. So in conclusion, there's no circle with an infinite diameter. We could, however, define a straight line as the circumference of an infinitely large circle. What possible benefit would that have though?

It appears to be a straight line. doesnt mean it is. seriously guys cmon.

>>3455801

You truly don't even have the slightest grasp of infinity, do you?

>>3455794
Graduate mathfag here, I've encountered limits on a lot of occasions, trust me (limits in metric spaces, topological spaces, pointwise limit of a function..)
I don't see a canonical definition of what the limit of a circle should be.

>>3455807
typical /sci/ asshole. stop assuming you are smarter than everyone.

>>3455810
It's a line at infinity, if the origin is zero. Obviously you can't have a circle of infinite radius on the real plane. But again, we're talking about limits.

Does trollpi bother you? Because the limit of that series IS a circle - it's just that the length of the members of the series is irrelevant.
http://qntm.org/trollpi

>>3455813

Obviously smarter than you.

>>3455810
>>3455822
In complex analysis, you use line integrals on a semicircle of infinite radius all the time.

>>3455824
you don't know me?

>>3455822
Why can't you? The real plane is infinite, so I think you could fit an infinite circle on it.

>>3455822

I didn't know about trollpi, but it seems to be one of those paradoxes that appear when people misunderstand the notion of a limit (in this case, uniform vs. pointwise convergence). That is the point I'm trying to make. You're looking at a circle in euclidean space. What is the limit supposed to be? Is it supposed to be a point set in some projective space? Then how does it arise?
I'm honestly curious here.

>>3455851
Sure, I'm just mainly pointing out that infinity itself is not part of the real plane. You have to modify the real plane to "add" infinity, and that changes things:
http://en.wikipedia.org/wiki/Line_at_infinity
http://en.wikipedia.org/wiki/Projective_plane

>>3455837

No no no, you have for each r>0 one semicircle, and to each of those radiuses you assign a value (the contour integral). Then you let that value go towards infinity as r -> infinity, you do NOT create some "circle of infinite radius".

>>3455873

Sorry, edit, I meant you take the limit of that value as the radius goes towards infinity

>>3455867
To be perfectly honest, I'm not enough of a mathfag to give you a proper definition and derivation.

But I used line integrals around arcs of circles with infinite radius in my complex analysis class all the time. The idea of an infinite-radius circle must have some legitimacy.

>>3455884
>>3455873
I agree that it's a limit, though I admit that my understanding of this is a little shallow.
>>3455822

>>3455543

Your perspective is limited and fixed.
Hence the increase in size of the circle will affect your perception of its curvature however that is only because of your own incapacity to understand your own limits.
The actual curvature is the same.
Evidence was acquired once we attained pictures of our planet from the Moon.
Your argument is invalid.

>>3455894

Yeah I took complex analysis last summer, I replied to that above your post. Intuitively, that's what you do - circle of infinite radius - but it's important to note the following:
You look at the series of the values of the contour integral and then take the limit of that, you do not take the limit of a circle and then use contour integration.

That is the whole dilemma: Interchanging limits.. This fails in cases like trollpi because the underlying objects are not "well behaved" enough

>>3455923
>The actual curvature is the same.
I don't think you know what curvature is.

>>3455927
I think I see your point.

In the case of trollpi, the limit of that series IS a collection of all points equidistant from the center, isn't it? Or is there some issue of missing points, like in the Cantor set?

>>3455873
It's radii.

wait, if a circle had infinite radius then it would be infinitely wide and infinitely tall, so how could it be a line (which has no width??)

>>3455928

How is that relevant?

In projective geometry you don't even have to look at "large circles", using a small one around infinity is perfectly valid.

>>3455940
What.

A circle is a set of points equidistant from a center, not an area. The "line" of a circle has no "width".

Another nice counterexample:
Picture the function f_n(x)=1 if x is in the interval [n,n+1] and f_n(x) =0 if not (this is a square with sidelength 1 on the real axis).
For every n, integration yields 1, so this is a constant series - the limit is 1.
If you take the limit of the function itself, it will be 0 (pointwise!!).
This is why - in general - integration and limits cannot be interchanged (you need a stronger concept of convergence to make this work).

And you're right, the limit is exactly the circle in the case of trollpi. However, it is a little trickier than that because computing the arclength requires the derivative, and the convergence of that is not guaranteed. Someone explained it in the comments

>>3455933

>>3455952

fuck you know what I meant nigger. Obviously it only makes sense if you're talking about arcs not complete circles which is what I'm saiyan

>increasing the diameter to infinite
>not normalizing the segment length
Why don't you just do the opposite and zoom in on your super curved circle to show that a circle is actually made of nothing but straight lines?

>>3455971

it's made of line SEGMENTS not actual lines what are you, a retarded?

It's not a troll. In physics you would totally use that kind of trick to simplify the equations locally. This is, of course, just linearization explained with hands.

But you can make this rigorous using a sequence of circular arcs. (t -> -n + n * exp(i * t / n)), t in [-1,1] is a sequence of circular arcs in the complex plane that converges uniformly to the segment [-i, i]

But it's not a straight line if you zoom out. Only from that point does the circle seem like a straight line.

You could just infinitely zoom out to see an infinitely large circle.

>>3456106

Easy, the point that is equidistant from every point on that circle segment is infinite meters to the left.

Your move, Mr. Bond.

Circles of radius r, with center distance r away from the origin, converges the the line. This convergence is C^\infty uniform on all compact subsets of the plane.

Not really much else to say. Better to think of things in terms of projective geometry, but the motivation for using it isn't so obvious.

>>3456607
>Easy, the point that is equidistant from every point on that circle segment is infinite meters to the left.

Are you sure it's not to the right?

Bitch?

>>3456796

Actually, it's both. I just said left to make it easily understandable.

This pic is why the observable universe is considered flat.

just fyi

>>3456801
Where the fuck did you hear that from?

When scientists reference a "flat" universe, they're not talking about geometry. A "flat" universe simply means that the net mass-energy of the universe is zero (as opposed to an open or closed universe).

>>3456798
And that's you, Failing.

>>3455619
That's because the speeds between bodies expanding themselves are less than the speed of light; yet the cumulative speed of all these expansions is in fact greater than the speed of light.

That's how I see it.