Circles Don't Exist? a theory of existance

[NNH1254 0]

I think they exist, I tried asking my pre-calc teacher about something a little like that once and he went off on a tangent (OMG that was the lamest joke on the face of the planet) that I didn't really follow. Math teachers are not people I like disagreeing with.Circle definitions are confusing, it all depends on which one you use. If I put a compass point in the corner of a ceiling (so where the ceiling and two walls meet) and go all the way around, it still meets some textbook definitions of a circle. Since it's one three surfaces though, and covering 90 degrees for each, it's only 270 degrees, so is it a circle or not?I don't know if this is what I hate about math or what I like about it.

[hitmanblood 0]

OK I'll begin waht the hell are you smoking Alex??? :)Joking, no you are not right people showed you mathematically that 0.9 is not equal to 1 and by the way circles do exist if not on our paper as geometrically they are infinite lines or even dots depends how you watch it. Circles do exist in nature and it is light in fact that is when light leaves star like sun if we disregard star winds and sun spots then you can see that light is leaving star in perfect circles and this has been proven physically. However you have to take also in concern that light has dual nature like wave and particle and in this sense to have perfect circle we are taking into account wave nature of light.So you see circles to exist.I'll finish this with quote: "Perfection is strong message, and circles are perfection".

[DeM0nFiRe 0]

Ok, I'll prove right now that circles do not exist.All regular flat shapes are maade of triangles right? This would mean that a circle is made up of an infinite amount of triangles right. In order for an infinite number of angles to not equal infinity when added, the measure of the inner most angle of each triangle is an infintecimal(or 0 repeating with a 1 at the end) right? this would mean that the remaining measures of the angles are 179.9 repeating.now, 1/9 = .1 repeating, correct? let's do some algebra:1/9=.1repeating <- now we'll multiply both sides by nine9/9 = .9repeatingNOw, we all know that anything divided by itself =1 correct? well, using if A=B and C=B then C=Awe'll see that if .9repeating = 9/9 and 1=9/9 then .9 repeating =1so that means that 179.9repeating is the same as 179+9/9, which means that the last angle, the one that is supposed to be an infintecimal, must be equal to the remaining ninths of 9/9 which means it's 0/9 which means that there are no other angles which means that a circle, by it's defintion of being closed regular shap, does not exist.

[dau1970 0]

i would like to retort with another question: is a straight line a particular case of a circle?imagine what happens if you take a circle and you start increasing its radius towards infinity... the curvature of the circle will start to flatten until, in the end, it's nothing but a straight line

Edited May 24, 2007 by dau1970 (see edit history)

[DeM0nFiRe 0]

No, a straight line is not a circle. The definition of a circle includes that it is a closed shape. A straight line holdds all the properties of a circle except the one. Circles are purely imaginary, as the definition is an impossibility.

[Plenoptic 0]

Well I've decided yes I see what you are saying, and in a perfect world they might not exist, but to me they do You see you can still draw them and have equations so to me they exist I am all confused right now and I guess you can say that they technically don't exist, or maybe we need a new definition for a circle, that way we don't have this problem. My mind will still be thinking about this for days now of how .999999999~ = 1 All the different ways to prove it so if you get in trouble with your teacher for "rounding" you can whip out a proof.

[matak 2]

Here's my 2 cents..

 

Circle is geometry construct, like dot, line triangle, and square, cube, sphere. When you look at geometry (Euclid 3D space) first you start with dot. Dot is definition of 1 dimension. Then you add, 2 dimensional space by adding plane. Plane is defined by one dot and 1 line that doesn't lie on that dot. Imagine it like paper without thickness. If you have dot on 1 place, and line on another, and that dot and line have no crossings or don't lie on each other, when you put that paper so that line lies on the paper and that paper touches dot, you got 2d plane.

 

Circle is 2 dimensional geometry construct, and can be drawn on that plane we got from line and a dot. It's defined by center and radius. if you define center as one dot and radius like one line of defined lenght eg 3cm, and you put one end of the line on dot, and rotate the other end of the line for 360°, trail which that end leaves is called a circle.

 

Most interesting number which you get from a circle is called Pi. (link)

 

Pi or π is a mathematical constant and a transcendental (and therefore irrational) real number, approximately equal to 3.14159, which is the ratio of a circle's circumference to its diameter in Euclidean geometry, and has many uses in mathematics, physics, and engineering. It is also known as Archimedes' constant (not to be confused with an Archimedes number) and as Ludolph's number.

Pi is used to calculate circles area.

 

Maybe you are confused with circles, beacouse you don't understand that number, and for further reading on mathematics, i would suggest you that you read about it, so that you don't start with some "crazy" inventions of your own

 

As for the 3d space, maybe later...

Edited May 27, 2007 by matak (see edit history)

[RedAlert 0]

For all that writing, matak sure doesn't do much reading. Try reading the posts in the thread before you add your "2 cents", or you might as well be responding to a thread on what you ate for breakfast.

[Carson 0]

Well, I think that there are no Circles in nature. Because they have to be perfect, they can only be formed by a computer.

[salamangkero 0]

Wokies, I think I saw where the fallacy is. (I already did a long time ago but it took me a while to get back to this thread)

 

Well if a circle has an infinite number of sides, that means each angle gets infinitely close to 180°.

No conflict here. I'll just repeat, each angle gets infinitely closer (but does not actually become) 180°.

 

Well this keeps on going 179.9, 179.99999999, until it hits 179.9-repeating.

This is impossible. It never hits 179.9-repeating. It just keeps on going from 179.9, 179.99, 179.999, etc but it is perfectly impossible to actually hit 179.9-repeating, that is an infinite number of 9's. How so? Well, how do you reach infinity? How do you count up to infinity? Infinity is, by nature, an exceedingly large and unattainable number. Besides, you said it yourself.

 

Well it is mathematically proven that .9-repeating, equals 1.

Therefore, 179.9-repeating is exactly 180, right? And, as we said before, each angle gets infinitely closer (but does not actually become) 180°. In other words, it will never hit 180, 179.9-repeating, 179+1 or any other representation of the same number.

 

Well if that is true, that means that circles are just strait lines.

If it were true, which, as we have seen now, is not the case. Circles cannot be equal to lines.

 

I told my calculus teacher this, and he just told me that that is similar to the theory that disproves motion: In order to move, you have to pass through an infinite number of points, and that of course is impossible. But that theory is obviously wrong because we can all move still.

I believe your teacher must be thinking of Zeno's paradoxes of motion. Yes, it is quite similar

[Liam_CF 0]

It's impossible to have an exact circle. It is an infinite number of lines and angles. At least, I think.

[sweet_princess 0]

i don't really quite understand that yet...i must be having a blonde moment because i didn't understand that cartoon thingy either

[Revan 0]

Perfect circles are impossible to create, so technically they don't exist because they can't be created. For Pi, the best we can ever come up with is an approximation.

 

As a calculus student, I have run into the .999... = 1 argument multiple times with multiple people. I always try to explain to them that it is not debatable, but accepted definition by mathematicians for the last 400 years. I will be more than happy to help you explain why. There have already been some proofs thrown around here varying from simple to somewhat more algebraic. Allow me to sum these up:

 

1/9=.111...

2/9=.222...

3/9=.333...

4/9=.444...

5/9=.555...

6/9=.666...

7/9=.777...

8/9=.888...

9/9=.999...

 

Since this is inductive in theory it's not a proof. So, let's use algebra to deductively prove this. This was done beautifully by alex7h3pr0gr4m3r:

 

1. x=.9... (Set x to .9...)

2. 10x=9.9... (Multiply both sides by 10)

3. 10x-x=9.9... - x (Subtract X)

4. 9x=9.9... - .9... (X is equal to .9 repeating, we stated that in step one, so this is legal)

5. x=1 (Divide by nine)

6. .9...=1 (Substitute)

 

Most people refute step 2 and 4, saying it does not correctly respect the concept of .9... however if one took the time to look in any algebra book this is taught and used by 8th graders everywhere to convert repeating decimals to fractions.

 

Still don't buy it? Ok then, let's assume .9... and 1 are different numbers. This means they have to have a difference.

1 - .9 = .1

.1 - .09 = .01

.01 - .009 = .001

On and on and on...

So in order for them to be different there must be 1 at the end of a set of infinite zeros. Yet this is logically impossible.

 

For anyone who has an elementary understanding of calculus, what is the value of (1/2)^x as x approaches infinity? Yes, it is indeed zero. The difference here is that .9... isn't approaching anything. It is simply itself, 1.

 

Finally, head over to Wikipedia and type in .999:

In mathematics, the recurring decimal 0.999… , which is also written as [...], denotes a real number equal to 1.

But Wikipedia is inaccurate right? People are changing it all the time, so there's no way .9... equals 1! Right Edited November 28, 2007 by Revan (see edit history)

[Maou_Tsaou 0]

I would say not...
A circle is a collection of contiguous 'points' equal distance from a 'centre' point. I didn't Google this definition, just based it on my understanding of what a circle is/is not. "An infinite number of angles on a straight line"... does not compute, Will Robinson...

This is hitting closer to the point. Pardon the pun
Infinagons don't cut it as infininty is just a way of saying I don't know. If you wanna throw infinities into the thing then you can renormilize it afterwards.
I believe the first time I ran across the little example for .9_ = 1 was in a book called "Infinity and the Mind" by Rudy Rucker.
The one I liked better from the first chapter is this;

Take a center-point.

Extend a line of unit 1.

Make the Circle r=1.

Now back to the point bit. What is a point? Well we simplly say they are dimensionless. Something like ghostmarkers in space. There can be an unlimited amount. Inifinate amount.

Okay then, what does this mean?

Take center-point from above.

Extend a line of unit 2.

Make the Circle r=2 (congurent?)

Now the questions are;
1 How many points make up the Circumfrence of Circle r=1?
2 How many points make up the Circumfrence of Circle r=2?
3 What is the ratio of the Circumfrence of Circle r=1 to the Circumfrence of Circle r=2?

In other words how can these figures Circumfrence consist of the same number of infinate points (radi from center-point for proff) when r=2's Circumfrence is twice that of r=1?





I found it a nifity read,




Maou

[fffanatics 0]

Circles exists for two reasons:1.) They are a conceptional idea for something that is round and connected in 2 dimensions. These obviously exisit because we see them everywhere everyday. However, how are they made and defined? This leads to reason 2.2.) 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.