Possible to draw a Perfect Circle???......

[Brandono]

I had my neighbors over a couple of days ago and I remember I said something like "it will go in a perfect circle" or something like that and I hear my brother and friend say their is no such thing. I then asked why and they kind of gave me that "I don't know but heard it in a smart math class so it's true" type of response. That will usually piss me off and cause me to argue until I get an actual answer from them for believing this. But nope, just ignorance and subject change.

This seemed to intrest me for some reason.

I did a few searches and of course the band came up more then anything. I did come up with a few forums talking about it and got a few things like:
Define perfect
No shape or line is perfect
Sometimes it's so close that it's good enough.
Something about pi
Protons may be perfect circles as gravity never changes
Perfect is something man cannot achieve
and a few other things but forget at the moment.

My definition of a perfect circle - If a circle existed with the EXACT curve around the whole thing and if divided by the diamiter, you would have EXACT equal space in every section that gets divided.

But my main question is, COULD it exist? The way I see it is as long as you can draw a perfectly straight line(or be able to duplitcate that same looking line), that would define the radius. So as long as you can duplicate that 360 times (We'll say that for the sake of 360 degrees) from the same point, that would make your circle.

I get the whole saying it's impossible (I hate too say impossible but VERY VERY difficult) to draw freehand because you have to be so precise. But in reality, such a thing could exist correct? Take my definition of a perfect cirlce, if it wasn't perfect but matched my deifintion(I know I contradict many things here but please keep an open mind), then the beggining of the circle would not match up with the end of the circle. If their is some math equation proving that this would happen I would understand, but haven't came accross it.

I think a lot of people confuse extremeley difficult and impossible a lot. Here's an example.

Make a closed shape with open area inside of it with 2 perfect straight lines(You can't bend them either or curve the paper or anything stupid like that). They can't be parallel because then it's either not closed or nothing inside of it. You can't slightly slant one because then you will have a slight open end.

This is where I would use impossible.

But for a perfect circle I believe that it CAN exist (Same curve around whole circle and same amount of area inside of itwhen cut through the exact diameter or it whereever and however many times). This is where I would find it extremely difficult and may not even be possible by man.

But then I also think that what if we had everybody in the world x100000 and they were just constantly drawing circles for 100000000000000 years, wouldn't it eventually come up.

Basically my question is, could it exist just extremely difficult for man to produce. Or does math prove it's not possible because all curves or areas will not be equal in a circle.

This also touchs on no two snow flakes are the same. Some of what I said apply to this also. And the fact that hackers say anything is possible to hack, just could take up to millions of years. Some would consider that impossible. Brute force hacking is basically just trying every possible password until the right one is reached.

Sorry had to get it off my chest.

 

[Omnis]

a circle is just a line around a point. They're obviously made perfectly with a compass or even with a pen attached to a piece of string attached to a fixed point.

 

[Brandono]

I guarantee you that those circles with a compass aren't .00000000000001 to the exact point everytime. Thats also another thing to consider. Our microscopes can only see so far as too how equal things are. For all we know, we can blow somthing up 10000000000 times and two lines may still look equal, but one could be off by .00000000000000000000000000000000000000000000000000000000000000000000000001.

Another question is how accurate can\do we have to be. We can obviously create a line with a certain length, so we can obviously do it again, just extremely difficult to match it's length 100%.

See my point, I know what a circle is, if it was a simple answer then I wouldn't have typed this much and made a thread. I bet I will have many different opinions on this.

 

[Wolfe]

So as long as you can duplicate that 360 times (We'll say that for the sake of 360 degrees) from the same point, that would make your circle.

Actually, duplicating it 360 times would produce a 360-sided shape...no, I don't know what the name for that would be.

In order for the circle to be perfect, the radius has to be "duplicated" an infinite amount of times.

But for a perfect circle I believe that it CAN exist (Same curve around whole circle and same amount of area inside of itwhen cut through the exact diameter or it whereever and however many times). This is where I would extremely difficult and may not even be possible by man.

But then I also think that what if we had everybody in the world x100000 and they were just constantly drawing circles for 100000000000000 years, wouldn't it eventually come up.

In my opinion, it is impossible for a truly perfect circle to exist, because as I said above, a perfect circle basically has an infinite amount of sides (or one curved side, if you want to look at it that way).

Even if you draw a very, very nice-looking, almost-perfect circle on a piece of paper, the line of the circle consists of paper particles and graphite/ink particles, of which there are a limited amount. Zoom in really close, and your "perfect" curved line turns into a squiggly, bumpy mess.

A perfectly cylindrical metal pipe? No way -- not only are there a limited number of particles, but metal machining isn't really perfect, so a pipe has (some-ridiculously-high-number) sides. A perfect circle on a computer screen? Nope, it's made of pixels.

Are sub-atomic particles perfectly circular/spherical? We can't know for sure, but if they're made of a limited number of smaller particles, then no.

Really, the truly perfect circle exists only as a concept. But as far as I'm concerned, anything that looks similar to one can be called "perfect." We don't have to take language 100% literally all of the time. Taking that into account, you were right, and your brother and friend were wrong.

 

[Omnis]

I guarantee you that those circles with a compass aren't .00000000000001 to the exact point everytime. Thats also another thing to consider. Our microscopes can only see so far as too how equal things are. For all we know, we can blow somthing up 10000000000 times and two lines may still look equal, but one could be off by .00000000000000000000000000000000000000000000000000000000000000000000000001.

Another question is how accurate can\do we have to be. We can obviously create a line with a certain length, so we can obviously do it again, just extremely difficult to match it's length 100%.

See my point, I know what a circle is, if it was a simple answer then I wouldn't have typed this much and made a thread. I bet I will have many different opinions on this.

That's because people tilt the compass. The string will work every time.

 

[OZZYGT]

In my opinion, it is impossible for a truly perfect circle to exist, because as I said above, a perfect circle basically has an infinite amount of sides

+REP for that wolfe. That's just what I was about to say. A perfect circle would have to have a radius or diameter duplicated infinite amount of times, and there is no such thing as that. So there cannot be a perfect circle, not with a professional compass nor with a "perfectly round shape" like the lid of a cylindrical container.


Ciao!

 

[Brandono]

Well I know the whole 360 lines isn't a circle (thats why I put for the sake of, so everybody would understand what I mean). I mean't doing that, then connecting those outisde points with equally curved lines. Basically just an example of what I mean. Draw a perfect circle, and you will have radius lines equal at every spot.

And it's not that I was saying they were wrong, just hate when people give me reasons based on what other people say with no information to back it up. This is how false information gets spread and how stupid people form.

Anyway, wolfe2x7 you did make some good points about the paper and atom thing. More and more things to consider.

The only thing that I keep thinking though is that as long as we have a .000000000000001 long curve thats consistent, if we created that the first time, then we are capable of doing it again, just extremely hard (Basically right before impossible). In reality it's basically not possible, but is capable of existing, just nobody to actually produce it.

I agree though, we don't always have to take language 100%, but just chose too hear to help my question out.

Thanks for the posts so far.

 

[Taurine]

That's because people tilt the compass. The string will work every time.

What if your string stretches?

 

[Omnis]

Use string that doesn't stretch. Wtf. This is how ancient civilizations did their circles.

Now, are we talking about drawing circles or having perfect mathematical diagrams?

 

[Der Alta]

So we've seen that you can come incredibly close to a perfect circle, but there itsn't really a perfect circle.

We've also discussed making multiple lines to create the appreance of a circle. Put enough small lines together and you can create a circle.

Shall we tip this further and wonder if you can create a perfectly straight line, to make the circles?

 

[Kylehnat]

Use string that doesn't stretch. Wtf. This is how ancient civilizations did their circles.

Now, are we talking about drawing circles or having perfect mathematical diagrams?

"Un-stretchy" string does not exist. And I doubt that ancient civilizations really cared whether their circles were perfect or not. Even if we think that their circles were perfect, they aren't, because we cannot measure a perfect circle any better than we can draw one.

As has been said: "perfect" does not exist in this world. A perfect circle (or any shape for that matter) exists only in theory. This does not mean that the concept is useless to us. We use the concept of perfection to make assumptions/approximations all the time. I just spent four years studying perfect systems. Was my education a waste becuase these systems do not exist in real life? Of course not. The theories can be used to design real systems, just like the theory of a circle can be used to design round things. Are your tires and wheels perfect circles? No. Do you notice/does it matter? Also no. Therefore, is our imperfect approximation of a circle good enough? Yes. Can we call it "perfect?" Sure, why not?

Is Maynard's version of A Perfect Circle correct? Hell yes!

 

[Jedi2016]

A perfect circle doesn't exist any more than the number zero. In theory, in imagined space, sure.. but not in reality.

 

[3-Wheel Drive]

When you split enough hairs, nothing is perfect. The world isn't exactly spherical, the Trans Siberian Railroad isn't completely straight, glass isn't completely smooth, and the "gold" rings in candy machines probably turn green in a month.

My point is, that after a certain point, it doesn't matter. If a ball bearing needs a diameter of 1.50mm to allow a pinwheel to run smoothly , it can usually be built within a tolerance of .01mm or so without grinding against other parts. What's a couple of nanometers, give or take? Nothing. After a point it isn't important. Things can't be made perfectly, the odds are just too low. But they can be built as perfect as they need to be to serve their purpose. You can't build a table complete 100% flat with zero variance on a even a molecular level, but you can build it flat enough to keep the things on it from sliding off, and that's all that matters.

Perfection is a relative term, as it is nearly impossile to get it exactly right, but can we see perfection as "Does it work as well as it possibly can in the conditions that are practical and realistic?" 100.000...% is not important, but getting as close as you can get to it, is.

 

[Omnis]

"Un-stretchy" string does not exist. And I doubt that ancient civilizations really cared whether their circles were perfect or not. Even if we think that their circles were perfect, they aren't, because we cannot measure a perfect circle any better than we can draw one.

So, apparently there is no point for this topic, as string will produce circles perfect enough for us not to tell the difference.

Ancient civilization cared enough to devise Pi.

 

[Gen.]

Are we forgetting the tool attached to the string can be tilted?

 

[Wolfe]

Are we forgetting the tool attached to the string can be tilted?

Not to mention that human hands are rarely rock-solid steady...

 

[VT]

Shall we tip this further and wonder if you can create a perfectly straight line, to make the circles?

In practicality it is impossible to draw a perfectly straight line, as lines continue to infinity in two directions at once. So you would have to be drawing a perfectly straight line going in two completely opposite directions for an infinite amount of time at the same time. Once you get to about the eight foot mark or so it becomes practically impossible to continue on any farther in both directions at once.

 

[nic_brix]

Why do lines have to have an infinite length VTGT07?

A straight line is simply the shortest distance between any two points.

It can continue infinitely in either direction. In practise it would be impossible (I.M.H.O.) to stop its angle of direction varying when trying to continue it for an infinite distance, thus making it no longer "perfectly" straight.

But the definition of a straight line does not include infinite length.




Back to the original question of this thread, though.
A "perfect" circle is possible/not possible depending on the definition of "curve".

- If a curve is made up of an infinite number of straight lines, then no, it is not possible to achieve a "perfect" circle. If this is the case, we can only perceive something to be "perfect", but strictly, mathematically and geometrically, it would be imperfect. It would be defined as a polygon.

- If, however the definition of a curve is a single line who's angle varies along its length, then a "perfect" circle is acheivable. Maybe not by man. But it would be possible.

So, in the end it comes down to your definition of "curve".
Alternatively, you definition of "perfect" or even "circle".

To come to a conclusion, I am using a Collins English Dictionary, published in 1985 (a long time ago I know). The conlusion I come to will depend heavily on the definitions from this dictionary.

Here are the definitions:

curve n.
1. a continuously bending line that has no straight parts.
[Remaining definitions omitted due to irrelevance to topic]

perfect adj.
3. correct or precise.
[All unrelated/unnecessary definitions omitted]

circle n.
1. a closed plane curve every point of which is equidistant from a given fixed point, the centre.
[Remaining definitions omitted due to irrelevance to topic]


So...
According to the Collins English Dictionary, published in 1985, a "perfect" circle is possible, as the definition of curve emplies that it is a single line whose angle varies along its length. Seeing as a circle is made up of a "a closed plane curve", it is made up of a single line, not lots, meaning a circle is not a polygon. The definition of perfect does not really affect anything in question.
This means a perfect circle is possible. Maybe not achievable by man at present, though.

Hope that makes sense.

Brix...

 

[Der Alta]

In practicality it is impossible to draw a perfectly straight line, as lines continue to infinity in two directions at once. So you would have to be drawing a perfectly straight line going in two completely opposite directions for an infinite amount of time at the same time. Once you get to about the eight foot mark or so it becomes practically impossible to continue on any farther in both directions at once.

Ahhh... But I didn't ask for a long line, I was just estimating a short line.

When you split enough hairs, nothing is perfect. The world isn't exactly spherical, the Trans Siberian Railroad isn't completely straight, glass isn't completely smooth, and the "gold" rings in candy machines probably turn green in a month.

My point is, that after a certain point, it doesn't matter. If a ball bearing needs a diameter of 1.50mm to allow a pinwheel to run smoothly , it can usually be built within a tolerance of .01mm or so without grinding against other parts. What's a couple of nanometers, give or take? Nothing. After a point it isn't important. Things can't be made perfectly, the odds are just too low. But they can be built as perfect as they need to be to serve their purpose. You can't build a table complete 100% flat with zero variance on a even a molecular level, but you can build it flat enough to keep the things on it from sliding off, and that's all that matters.

Perfection is a relative term, as it is nearly impossile to get it exactly right, but can we see perfection as "Does it work as well as it possibly can in the conditions that are practical and realistic?" 100.000...% is not important, but getting as close as you can get to it, is.

Now we're getting somewhere. Tolerance. Within set tolerances we can achieve a perfect circle.

After all... On a long enough timeline, the survival rate for everyone drops to zero. In other words, given any measurement, it's not always going to be exact.

 

[Pupik]

Ancient civilization cared enough to devise Pi.

Pi is a constant, and it took 2000+ years to figure out that it was a repeating decimal to something like one million decimal places. However, there's no way to way to use numbers that precise, as there's error in almost everything used in the real world of measurement, physics, engineering, et cetera.

In the world of mathematics, where there is no use for "error", you can go on and on infinately, and deal with concepts all day long. To me, pi is still quite fascinating. No matter how big or small a circle, it's still the same ratio of diameter to circumfrence.

There are no straight lines in reality, no perfect circles, and no prefect measurements. But if do not have a concept and definition of what a circle or line is, then communication is worthless; how would we have a word for "round thing" or a "straight thing". Without communication, we're animals. Without concepts we won't have any corresponding reality, definitions break down and communication sdfaoikj enm52 fm;epo$!

See!?!

 

[Brandono]

So, apparently there is no point for this topic, as string will produce circles perfect enough for us not to tell the difference.

Ancient civilization cared enough to devise Pi.

Well I wouldn't say pointless. It looks like you learned something.

But I agree with nic_brix, it all depends on your definition and may even not be possible by man, but could exist without any math proving it imperfect.

 

[Omnis]

Maybe the universe is one giant perfect circle.



UH OH, here we go!

 

[Der Alta]

Maybe the universe is one giant perfect circle.



UH OH, here we go!

Ahhh.. Yes, the circle of life.

 

[nic_brix]

Maybe the universe is one giant perfect circle.

I'm sorry, but I was under the impression that the universe has more than 2 dimensions (or 3 if you're being fussy and want to include time as one).

Anyway, If string theory is correct there are about 20... but I'm drifting off topic.

 

[Omnis]

I'm sorry, but I was under the impression that the universe has more than 2 dimensions (or 3 if you're being fussy and want to include time as one).

Anyway, If string theory is correct there are about 20... but I'm drifting off topic.

Yeah, but the circle is so huge (you know... because it's perfect) that it has an infinite amount of dimensions in one.

 

[nic_brix]

Yeah, but the circle is so huge (you know... because it's perfect) that it has an infinite amount of dimensions in one.

Mmmm... There might be some twisted logic in there somewhere.

The point I was trying to get at is that a circle has just 2 dimensions... I think you meant a sphere.

 

[the Interceptor]

Yeah, but the circle is so huge (you know... because it's perfect) that it has an infinite amount of dimensions in one.

I can't help the feeling Omnis is not entirely serious.

 

[Omnis]

Mmmm... There might be some twisted logic in there somewhere.

The point I was trying to get at is that a circle has just 2 dimensions... I think you meant a sphere.

So you're saying that if you line up a bunch of spheres around a single point, they don't create a circle?


I think we're breaking ground here, people.


edit: god forbid that circle be perfect...

 

[Iceman]

Another thing to consider; is there any way to actually know if a circle is perfect or not? Are any measuring devices perfect?

 

[3-Wheel Drive]

Why do lines have to have an infinite length VTGT07?

A straight line is simply the shortest distance between any two points.

It can continue infinitely in either direction. In practise it would be impossible (I.M.H.O.) to stop its angle of direction varying when trying to continue it for an infinite distance, thus making it no longer "perfectly" straight.

But the definition of a straight line does not include infinite length.

A line must continue indefinitely. A line is definded as "a straight curve on which that passes between any two points, and extends infinitely in either direction". Lines do not have endpoints. What you are thinking of is a line segment, which is defined as "a part of a line that is bounded by two end points, and contains every point on the line between its end points". Line segments always have finite length, which include all "lines" that are drawn by human or computer. So, a line must be defined to include infinite length, and they do provide the shortest distance between two points in the form of a line segment.