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IF i was a 1 dimensional being living in a 1 dimensional Universe being a circle. 
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#1
Jan1912, 07:09 PM

P: 22

How could i mathematically proove that im living on a circle. Almost got it last night , just need an insight to figure out an equation.
Ty. 


#2
Jan1912, 07:12 PM

P: 10

Circle is object in two dimensions!



#3
Jan1912, 07:16 PM

P: 22

the circle being 1,2,3,4,5 or 6 dimensions is not important. I need the maths to get me there.



#4
Jan1912, 08:25 PM

Astronomy
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IF i was a 1 dimensional being living in a 1 dimensional Universe being a circle.
So a ring can be defined and studied without assuming the existence of any surrounding 2D space. However it is trivial. there is no intrinsic way to define a curvature that could be nonzero. There is (at least in my opinion) no way that the 1dim creature can discover the topology of his world unless he makes a voyage of exploration. He must circumnavigate his world. He must tell his 1D friends to stay at one place, to mark that place, and then he must travel as far as necessary in one direction. when he sees his friends again he will know that it is a ring. 


#5
Jan2312, 01:34 PM

P: 53

surely a ring has more than on dimension, two at the least
A 1D universe would just be a line if a 1D being did try to determine the shape of its universe by marking a position and seeing if he came back upon himself suggests that the universe is 2D or greater. A 1D universe would not have a shape to it. Or am I mistaken? show me a shape that has 1 dimension As for the Op, I have no idea how a 1D being would be able to prove he is on a 1D universe using mathematics EDIT  It has come to my attention that even a line is a 2D object. I cannot see or imagine how a 1D universe would work, it would have no shape in any sense of the word, making your question impractical. 


#6
Jan2412, 12:19 AM

P: 534




#7
Jan2412, 04:12 AM

P: 53

I do not see how a 1 dimensional universe can loop back on itself without the presence of an extra dimension I imagine a 1D universe to consist of just length, without width or depth, without these dimensions their would be no discernible shape to it. Have I misunderstood something here? 


#8
Jan2412, 06:17 AM

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#9
Jan2412, 06:56 AM

P: 53

But how does this apply to the Op's question and a 1 dimensional existence.
How can there be topology in the 1D 


#10
Jan2412, 07:50 AM

P: 534

See Fig 1. of this article.



#11
Jan2412, 07:59 AM

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#12
Jan2412, 08:14 AM

Astronomy
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PF Gold
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http://physicsforums.com/showthread....07#post3724707 As I see it, some of these elementary math questions might be better pursued in the math forum. Or in Relativity forum. After all, cosmology (the topic here) is based on GR which in turn is based on differential geometry as developed in the 19th century by Riemann. If you want to discuss the basics of the math foundationsthe language used to formulate cosmic modelsdifferential geometrymaybe this is not the place. 


#13
Jan2412, 08:23 AM

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#14
Jan2412, 08:25 AM

Astronomy
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PF Gold
P: 23,121

http://profmattstrassler.com/article...icconfusions/ I spelled your Figure 1 link out simply to amplify: his post is "Big Bang Classic Confusions" and we could make regular use of it here, it deals with several issues besides the dimensional and topological one. 


#15
Jan2412, 08:32 AM

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#16
Jan2712, 08:29 AM

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P: 322

How can a straight (one dimensional) line loop around anything ? Doesn't make sense to me. Or has 'straight' been redefined to mean 'slightly curved' ?



#17
Jan2712, 08:38 AM

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#18
Jan2712, 08:39 AM

P: 38

Takes the numbers 1 to 10. That is a straight, 1 dimensional line. Now when you count to 10, what's next after 10? Stop or loop back to 1? I'm not sure what a 'not straight' 1d line would be like... Just a guess, but I would suppose it would be a nonlinear line. As in not all points are evenly distributed. Count from 1 to 10 but skip 3,4 and 7. 


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