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## So, Do Circle's Exist?   29 members have voted

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Math is tricky. From what I was taught, a line is just a bunch of points. Now what is a point? It's hard to define. A circle is similar. It's easier if you just take math for what it is and don't think too deeply. But I do encourage thinking, and you bring up a good point. Hang on with me here as I give you my explanation, but remember I'm just in geometry. 179.99 etc. doesn't equal 180, and never will. It will come very close to 180, but it will never reach it. Therefore, a circle can't be a line because it never is 180. Just my ideas, you can think what you want.

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Ok I've got the equation: (lets say underlined numbers mean repeating)

x=.9 - Set x to .9 repeating

10x=9.9 - Multiply both sides by 10

10x-x=9.9-x - Subtract X

9x=9 - x is .9 repeating, so subtracting it from 9.9 repeating gives you 9

x=1 - divide by nine

.9=1 - Substitute

.9 times 10 equals 9 not 9.9

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Why are you guys talking all mathematicly? A circle is the thing that goes on top of stick figures. Or this ( o ) That is a circle I do not really understand all these numbers and stuff? ##### Share on other sites

A circle is just an infinite number of angles on a line right?

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...

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Well this keeps on going 179.9, 179.99999999, until it hits 179.9-repeating. Well it is mathematically proven that .9-repeating, equals 1.

It is not mathematically proven that .9-repeating equals 1. They tell you to round it off, which would equal 1. The only reason they tell you to round it off is so you won't have to write the number down. Ok I've got the equation: (lets say underlined numbers mean repeating)

x=.9 - Set x to .9 repeating

10x=9.9 - Multiply both sides by 10

10x-x=9.9-x - Subtract X

9x=9 - x is .9 repeating, so subtracting it from 9.9 repeating gives you 9

x=1 - divide by nine

.9=1 - Substitute

I think you messed up somewhere in your equation... Like , don't you divide here instead of multiplying? Do the opposite?

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Well to continue my annoying streak , I'd like to point out that it is mathematical impossible for .9 repeating to equal 1. It's like saying in the equation 2^x=y that y could equal 0.Anyways, it's an interesting idea, but still not going for it.

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.9~ = 1, and anyone who doesn't think so should go back to school and take advanced math.Here are some proofs...pick one you can understand:Let us assume x = .99999~Now we know that when we multiply something by 10, wemove the decimal one place to the right.so 10x = 9.9999~ There is no 9 lost by doing thissince there are an infinite number of them.Now we do simple arithmetic10x - x = 9.999~ - .9999~9x = 9 This is allowed because every 9 after thedecimal will cancel with another 9.x = 1 and x = .999~ so 1 = .9999~.9999~ = .9 + .09 + .009 + ....here we represent .9~ as an infinite sumsum[i:0->inf.](.9*.1^i)We know how to solve infinite sums.sum = .9/(1 - .1) = .9/.9 = 1Since we said the sum was initially .9999~, we canconclude that .9999~ = 11/3 = .33333~This is true, and can be proven with an infinite sumas above.3*1/3 = 3*.33333~1 = .99999~We are allowed to multiply by 3 because no part isgoing to carry over to the next part. Thus, every partof the decimal will increase by factor of 3, making ita 9.The real numbers are defined as limits of Cauchysequences of rational numbers.*A rational number is a fraction of two integers*A cauchy sequence is a sequence x(1), x(2), ... suchthat for every integer n there exists an integer msuch that |x(j) - x(k)| =< 1/n for all j,k >=m.Two Cauchy sequences x(1), x(2),... and y(1), y(2),...are considered equivalent if for every integer n thereexists an integer m such that |x(k) - y(k)| =< 1/n forall k>=m.Let x(j) = 1 - (1/10^j)Let y(j) = 1.I'll leave it to you to check these are Cauchysequences.These two sequences are equivalent:Given some integer n, |x(k) - y(k)| = |1-(1/10^k) - 1|= |1/10^k| =< 1/n if 10^k >= n. So we'll set m ={smallest integer greater than log(n)}.Thus the sequences .9, .99, .999, ... and 1, 1, 1...are equivalent, so they have the same limit, namely,.999~.0.9~ = 0.9 + 0.09 + 0.009 + 0.0009 + ...S = 0.9~S = 0.9 + 0.09 + 0.009 + 0.0009 + ...S = 0.9 + (1/10)[0.9 + 0.09 + 0.009 + ...]S = 0.9 + (1/10)S(9/10)S = 0.9S = 1Therefore, 0.9~ = 1.If two numbers are not equal, there are an infinitenumber of numbers between them. Give me a numberbetween .9999~ and 1.All repeating and terminating decimals can berepresented as fractions. If .999~ is not representedby 1, what fraction does represent it?

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I like to point out that I lost all faith in the circle now with all this math and it's existence nonsense . So to help mess with people's mind's even more check out this wonderful info about the circle.
https://en.wikipedia.org/wiki/Circle

Of course through my researching this wonderful thought there are several other sites that would agree .9999~ = 1

here

http://forums.xisto.com/no_longer_exists/

and here

http://forums.xisto.com/no_longer_exists/

But like I said you all ruin the beauty of the circle now I to rely on a triangle and a square to get me through life . but to stay on topic just a bit after reading these posts and those 3 websites I would have to agree especially with this part

Here are some proofs...pick one you can understand:Let us assume x = .99999~
Now we know that when we multiply something by 10, we
move the decimal one place to the right.
so 10x = 9.9999~ There is no 9 lost by doing this
since there are an infinite number of them.
Now we do simple arithmetic
10x - x = 9.999~ - .9999~
9x = 9 This is allowed because every 9 after the
decimal will cancel with another 9.
x = 1 and x = .999~ so 1 = .9999~

The math teacher followed the same line of thinking, in which I conclude that .99999~ = 1 is both a true and false statement. Meaning that if you round up you will get 1; however, since the number is always repeating itself then it is not a true solid number (can't think of the word for it but you math geeks know what I am referring to). You call this a enigma in itself and odds are you would have to apply occam's razor to make the most sense out of this enigma.
Edited by Saint_Michael (see edit history)

##### Share on other sites Love this post. I go with the "smoking" answer, and it's winning so... I can't discuss on this but I think a circle it's a circle and yes, it's also a polygon with so many angles that the eye can't see them and the final look is curved and sharpened. Both things, or one thing forms another, whatever. I need more inspiration to answer properly.

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But like I said you all ruin the beauty of the circle now I to rely on a triangle and a square to get me through life . but to stay on topic just a bit after reading these posts and those 3 websites I would have to agree especially with this partThe math teacher followed the same line of thinking, in which I conclude that .99999~ = 1 is both a true and false statement. Meaning that if you round up you will get 1; however, since the number is always repeating itself then it is not a true solid number (can't think of the word for it but you math geeks know what I am referring to). You call this a enigma in itself and odds are you would have to apply occam's razor to make the most sense out of this enigma.

If you and your math teacher really think that, then neither of you understand what infinity is. .9~ is not a process; it's not growing. It's a number that's exactly equal to 1 without rounding.

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Whoah! That was some...whooh! I don't think I can add anymore to what was already said. It's kinda hard to stomach, 0.999... being equal to 1 and all, really, but I suppose advocates of the Ptolemaic model felt the same with Copernicus' heliocentric model.

Personally, I don't believe in the existence of circles. They are, for all we know, nothing more than constructs in the mind of sentient species, like humans, for example. Why is that? Because circles have no thickness! They have height and width, being in 2D but they have no thickness. Their z-dimension is zero. In our world, it would have to be a loop of wire in the shape of a circle but having an infinitesimally small, even non-existent, thickness.

Oh yeah, for that matter, I don't believe in squares and triangles too. As a matter of fact, I could be audacious enough to claim that polygons do not exist. So, sorry, Saint_Michael, I suppose the beauty of triangles and squares have also been dispelled I do concede, however, that what we have here in the real world are approximations of a circle, or polygons, for that matter ##### Share on other sites

If you and your math teacher really think that, then neither of you understand what infinity is. .9~ is not a process; it's not growing. It's a number that's exactly equal to 1 without rounding.

That not my math teacher I am referring to, I was referring to the teacher in those links has follow the same procedure as stated by your previous post. Now just remember what I was referring to in my last post since .9999~ is not a whole number and not solid so a minor correction on that.

Well think about it though .9999~ is a fraction right? and if that 9 keeps repeating itself in just basic math then it will never equal 1. But I think it was mention somewhere you have to be high up there in math; like trig calculus and even physics. So I would say my state is true that depending on the situation that .9999~ is being used it will never be a true whole number, but it could be especially when you go into margin of error +/-. Taking this stats class last semester, .9999~ would become a whole number so to have none of those factions appear in statistics reports and thus the margin of error would go into effect. But hopefullly I can bump into this math teacher at college and ask him about it and see what he comes up with. I think he's been a math teacher since about 30 years so I would say he could give a good solid answer on this.

Whoah! That was some...whooh! I don't think I can add anymore to what was already said. It's kinda hard to stomach, 0.999... being equal to 1 and all, really, but I suppose advocates of the Ptolemaic model felt the same with Copernicus' heliocentric model.
Personally, I don't believe in the existence of circles. They are, for all we know, nothing more than constructs in the mind of sentient species, like humans, for example. Why is that? Because circles have no thickness! They have height and width, being in 2D but they have no thickness. Their z-dimension is zero. In our world, it would have to be a loop of wire in the shape of a circle but having an infinitesimally small, even non-existent, thickness.

Oh yeah, for that matter, I don't believe in squares and triangles too. As a matter of fact, I could be audacious enough to claim that polygons do not exist. So, sorry, Saint_Michael, I suppose the beauty of triangles and squares have also been dispelled happy.gif

I do concede, however, that what we have here in the real world are approximations of a circle, or polygons, for that matter happy.gif

This isn't the matrix lets try and stay in the physical plane . It reminds me of a Star Trek episode where they mention a dodecahedron, which I believe is like 26 sides shape or something like that, but of course now we would be going into physics about containing energy and what not.

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A circle is really just an infinite amount of triangles. Technically circles actually do have sides. to make any regualar shape you use triangles. And as the number of triangles increases, the length of the base of each triangle decreases(assuming you are keeping the same area). this means that as the number of triangles approaches infinity, the length of the side approaches an infinitecimal.

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