Circles Don't Exist? a theory of existance

[Maou_Tsaou 0]

2.) Circles exist because an equation can be determine in in which for every x value of a circle defined by a radius r, there is a value for y. Since an equation exists, a circle does exist. Your point about there being an infinite number of points is so wrong because if you use that argument, a line doesnt even exist because a line contains an infinite number of points.

While I agree that the example dosn't show that circles don't exist, the above has me scratching my head for two reasons.

First, a line contains an infinite number of points.

Second, the only value math has as a formal system is it's ability to help us model "objective" reality, whatever "That' is.
Goodel showed the limits of formal systems for capturing "Truth".
I suspose what I'm trying to say is that I don't see how an equation equaits to proff.


Anyway, Rucker used this as a springboard into Transfinite Numbers.
Aelf-One and such.


I didn't mean to imply no Circles.

Sorry.






Maou

[Animator 0]

Your approach is wrong. You're basically zooming in so close to inspect the edge (trying to get the infinite 0.9999999....) that you're claiming to see a straight line. Stand back and the angle looks smaller.

[Nabb 0]

A circle is the set of points in a plane that are equidistant from a given point O

Would help to define a circle correctly

And by the way, the proof that 0.999... = 1 does bring up a point
Let ...999 = x (an infinite string of nines).
10x = ...9990
x - 10x = 9
x = -1
... this forms the basis of integers in computing!
(no, I doubt that, but it is a striking resemblance!)

[Erdemir 0]

A circle is a collection of contiguous 'points' equal distance from a 'centre' point.

I agree with this. And one more thing we can describe point as everything and nothing.
This is from wikipedia

In geometry, topology and related branches of mathematics a spatial point describes a specific point within a given space that consists of neither volume, area, length, nor any other higher dimensional analogue.

Point has no volume, no area, no length....
Point is undefinable, and a circle is collection of points (not lines), so circle is also undefinable.

Your opinion will be clear when you can describe what the point is.

[FreedomOverdose 0]

as previously said, math is very tricky. You can't always apply the following statement (to be honest, can't remember the property's name in english )a=bb=c___a=cSo, you cannot mathematically proovee that 0.9- equals 1. If so what would 1-0.00000(infinite zeros)0001 be??see, this is veery tricky :)edit: so, let's suppose that circles really are straight lines. How can You explain that a circle(a straight line as supposed) does never overlap with a straight line? In fact, is tangent or it intersects it. This leads that a straight line NEVER overlaps with another straight line, which is wrong =>circles aren't just straight lines!

Edited September 8, 2008 by FreedomOverdose (see edit history)

[minimcmonkey 0]

Well, however close it may be, 179.9999999999999999999999999999999(recuring) is not quite 1So, there is such thing as a circle, well i think there is.

[iGuest 3]

if a point has no length, no volume, and no area. Then a point does not exist.

[cyber_electrons 0]

What if we define a circle as allpoints have equal distance from the centre, ie all radius of a circle is the same, and not associating the interior angle? And obviously, there will be infinite number of points. I really don't think there is a need for calculating the interior angle unless it will help in a practical situation. But like someone said eearlier, I would encourage the good thinking...

 

For practical use, I think the precise interior angle would be irrelevant.

[triplebtalk 0]

I am going to say no on the basis of a circle being made up of a whole ton of little dots which are positioned into a shape thus creating the circle. The theory you present is very similar to 6 not having a square route, your calculator gives you a small number, but the actual number goes on forever, in no apparent cycle. Any shape is basically just a lot of dots positioned in what we call a shape, the dots could be replaced with a line but I am unsure which it is made up of. The idea that angle must create a circle is slightly clouded, if a circle was made up of dots then where would the angles fit in?

[networker 0]

In a way the theory is true because any circle it seems would still have littlejagged edges and stuff sticking out,so the idea of a perfect circle is reallyhard to do.I mean,just try making a circle in microsoft paint and one gets something circular butfar from perfect,

[iGuest 3]

x cannot be repeating. it is a constant.Circles Don't Exist?

You cannot set x to .9 repeating. That is not a constant not matter what x has to be an exact number. That is the flaw in your equation.

-reply by Isaac Smith

[iGuest 3]

Circles only exist as symbols within the mind of the observer. Mathmatically they do not exist, every possible concieved formula for calculating the area of a circle is an approximation, even the calculation for the perimeter of a circle is an approximation. In order for someone to prove to me they do exist, that person would have had to create a new measurement system entirely, luckily the mayans had a jump start(they could measure planetary orbits more accurate then us until we finally invented lasers.. put that in your pipe and smoke it.), unfortunately most of their mathmatics have been lost in time. And sadly I have found many mathmatical forumlas to be quite flawed and incomplete in my opinion; another such flaw I believe math to have is the understanding of i. But we'll talk about that perhaps another time.

[iGuest 3]

Circles only exist as symbols within the mind of the observer. Mathmatically they do not exist, every possible concieved formula for calculating the area of a circle is an approximation, even the calculation for the perimeter of a circle is an approximation. In order for someone to prove to me they do exist, that person would have had to create a new measurement system entirely, luckily the mayans had a jump start(they could measure planetary orbits more accurate then us until we finally invented lasers.. put that in your pipe and smoke it.), unfortunately most of their mathmatics have been lost in time. And sadly I have found many mathmatical forumlas to be quite flawed and incomplete in my opinion; another such flaw I believe math to have is the understanding of i. But we'll talk about that perhaps another time.

 

Finally someone who is talking sense. It are all approximations, 1/9 is approximate 0.111(infinite). That's why you were (or at least I was) thought that fractions are for maths and decimals are for physics and other practical things. Also we had to leave fractions and roots at the end of our calculation to show that its not approximate but accurate.

 

Concluding: math is all about theory and perfection, just like a circle!

[iGuest 3]

Finally someone who is talking sense. It are all approximations, 1/9 is approximate 0.111(infinite). That's why you were (or at least I was) thought that fractions are for maths and decimals are for physics and other practical things. Also we had to leave fractions and roots at the end of our calculation to show that its not approximate but accurate.
Concluding: math is all about theory and perfection, just like a circle!

Math IS all about theory and perfection. Circles, on the otherhand...

They are a completely different branch of mathematics then algebra. You may be able to prove that 0.9999~ = 1 algebraicly, but in our 3-dimesional world it will never hold true. Our minds think in 3 dimensions, and cannot comprehend infinity. Then arises the question does infinity actually exist? I am not compenent enough to answer, yet.

A circle is a polygon with an infinite amount of sides. Therefore, circles do not exist in our 3-dimensional world. Maybe they exist on some higher plane of beings with greater intelligence than us, but if you take any 'circle', no matter how 'curved' its circumference is, you will always be able to break it down into an incredibly huge number of straight lines, but not an infinite number of straight lines.

So, every cirlce in our universe therefore cannot be perfectly circular. All the cirlce theorems, and all properties of a circle are hypothetically applied to perfect cirles, yet perfect circles don't exist. The length of a circles diameter is Pi x the diameter, and here we discover something very interesting.

Now, lets assume there is no flaw in my arguement that circles don't exist. So, assume that a perfect circle does not exist.

Therefore, does Pi exist? No, it does not.
Why have we got a transcendential number that infinitely produces a long string of decimals with no pattern of any kind? Because we have derived this number from an impossible shape.
Again, I will refer to our 3-dimensional world. Because circles here will be extremely close to perfect roundness (this term is used loosely, as no matter how close circles are to perfect roundness it is never achieveable), the ratio of their circumference to their diameter will be extremely close to Pi, but never exactly reach it either.

From my memory, Pi is:
3.14159265358979323846264338327950288419716939937510582097497759230781640628620899862603421134825... (i think), yet a ratio between a circles cirumference and diameter may only equal:-
3.1415926535897932384626433832795028841972 and we logically cannot rule out this possibility now. Do you see?

Back do the question. Do cirles exist?
Circles are something man has created for amusement, amoung other things. But saying 'do cirles exist' really depends on your own definition of a circle. Therefore, based on your own veiws, beleifs and logic, you decide whether or not they exist. I have shared my veiws with you.


If you wish to dicuss this statement with me any further, you can contact me on 07784207942, which is my phone number... as i do not plan on returning to this thread again. Farewell.

[iGuest 3]

"Then arises the question does infinity actually exist?"

This is precisely where the problem lies! What is infinity? Does infinity truly exist? Are there as many prime numbers as there are numbers? Of course. But if the number of prime numbers equals the number of numbers because both are infinite, there will always be an extra item beyond the last. There is no completeness. It turns ad nauseam - I say there is no such thing as infinity. It cannot be defined as it becomes equivocal. A mathematician rambles on about a "number series" when the question of infinity is raised. There can theoretically be an infinite number by counting sets. But still, there will always only be large numbers or small numbers, logically, physically, and in reality. It all goes back to Spinoza's sixth axiom, and Zeno before him, and even Heraclitus before him. We haven't really learned anything since, just learned how to apply everything...almost everything.

If infinity exists, a perfect circle can exist. But it doesn't.