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Author Topic: Can a ring be made out of straight lines?  (Read 1728 times)

Offline yor_on

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Can a ring be made out of straight lines?
« on: 29/04/2013 03:04:05 »
That's one fundamental thing I've been wondering about for the longest time. So what do you think, can it? Or can we prove that circular figures must exist, in and by themselves, as some fundamental scaled down 'bit'? It is also a question of smoothness to me, as in a 'bit' universe it seems more appropriate, to me, for them to be straight lines :) Weird stuff, and I'm wondering about it.


 

Offline yor_on

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Re: Can a ring be made out of straight lines?
« Reply #1 on: 29/04/2013 03:10:57 »
And, what would a 'point' be from that perspective?
 

Offline Pmb

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Re: Can a ring be made out of straight lines?
« Reply #2 on: 29/04/2013 03:26:42 »
That's one fundamental thing I've been wondering about for the longest time. So what do you think, can it? Or can we prove that circular figures must exist, in and by themselves, as some fundamental scaled down 'bit'? It is also a question of smoothness to me, as in a 'bit' universe it seems more appropriate, to me, for them to be straight lines :) Weird stuff, and I'm wondering about it.
I'm not entirely sure of what you're asking but I think the answer is no. At least not in Euclidean space. A line is a geometric object which, by definition, does not close on itself. The term "point" is something that you have to know what it is since it can't be defined in terms of something more basic.
 

Offline evan_au

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Re: Can a ring be made out of straight lines?
« Reply #3 on: 29/04/2013 10:51:27 »
It is possible to create a circle of radius X as a set of points like this: "The set of points in a plane surface which are distance X from a specific point called the center."

The same type of logic creates:
  • More complex curves like a Lissajous figure: "The set of points (x,y) described by the equations x=cos(θ) and y=cos (3θ)."
  • Or a sphere: "The set of points in a 3D space which are distance X from a specific point called the center."

Since a point is just a line of zero length, it is also possible to create a circle from an infinite number of zero-length lines.
 

Offline yor_on

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Re: Can a ring be made out of straight lines?
« Reply #4 on: 29/04/2013 14:39:43 »
Yes, but it becomes very tricky to imagine something of zero size creating a finite length? And there I would say it won't matter how we refer to it, as being circles or straight lines? And in a 'bit universe' we do seem to expect a finite definition of a length (Plank scale), don't we?

I do like points, but dimension less points, of no scale, defining one?
How do they do it, if they do it?
 

Offline yor_on

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Re: Can a ring be made out of straight lines?
« Reply #5 on: 29/04/2013 14:41:53 »
Yeah Pete, the definition exist, I'm just questioning how we know?
And define it practically, using scale to wonder about it.
 

Offline Pmb

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Re: Can a ring be made out of straight lines?
« Reply #6 on: 29/04/2013 17:16:45 »
Yeah Pete, the definition exist, I'm just questioning how we know?
And define it practically, using scale to wonder about it.
The term point is not defined in geometry. Its a basic term in which other terms are defined. If you saw a definition somewhere then it was meant to give a person a sense of what one means by a point but I can priomise you that such a definition is circular. Another term which is undefined is "set."
 

Offline yor_on

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Re: Can a ring be made out of straight lines?
« Reply #7 on: 29/04/2013 19:15:53 »
I was thinking of a line Pete. The definition exist, but is it enough in itself? If you want a smooth universe then? And if you want a 'bit universe'? The universe exist, and so do straight lines, and bent, but what do they scale down to?
 

Offline Pmb

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Re: Can a ring be made out of straight lines?
« Reply #8 on: 29/04/2013 19:51:41 »
I was thinking of a line Pete. The definition exist, but is it enough in itself? If you want a smooth universe then? And if you want a 'bit universe'? The universe exist, and so do straight lines, and bent, but what do they scale down to?
I question any definition of "line" too. It requires the notion of a point being "between" to other points and "between" is another undefined quantity which we're supposed to know. One can define a line analyticfally as all points (x,y) which satisfy the relation y = mx + b but to draw a line you need a Cartesian coordinate system which is constructed using lines so that's circular. See where I'm going?
 

Offline yor_on

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Re: Can a ring be made out of straight lines?
« Reply #9 on: 29/04/2013 19:58:54 »
Yep :)
 

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Re: Can a ring be made out of straight lines?
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