How can a 1-dimensional being prove they live on a circle?

[minio]

Similarly in a two dimensional infinite cylindrical universe, the inhabitants measure each triangle to sum up to 180 degrees, intrinsically the universe has *flat* geometry.

I just want to ask - this is true only for cylindrical geometry, not for sphere, right?

 

[rustynail]

Why are you imposing "straight" on the concept of one-dimensional? The OP correctly did not.

I'm sorry for taking this argument 2 days back, but I think I can see the problem OP is having concerning curved 1-dimensional lines. Being curved implies being oriented in a different direction, and thus, along a different axis. So to give a description of a point along a line in an ℝ^n space would require n different coordinates. But, correct me if I'm wrong, even though the line is described in an ℝ*^n space, the line itself has only one dimension, it's length.

 

[daveb]

I'm sorry for taking this argument 2 days back, but I think I can see the problem OP is having concerning curved 1-dimensional lines. Being curved implies being oriented in a different direction, and thus, along a different axis. So to give a description of a point along a line in an ℝ^n space would require n different coordinates. But, correct me if I'm wrong, even though the line is described in an ℝ*^n space, the line itself has only one dimension, it's length.

Correct! Very astute observation!

 

[DaveC426913]

I'm sorry for taking this argument 2 days back, but I think I can see the problem OP is having concerning curved 1-dimensional lines. Being curved implies being oriented in a different direction, and thus, along a different axis. So to give a description of a point along a line in an ℝ^n space would require n different coordinates. But, correct me if I'm wrong, even though the line is described in an ℝ*^n space, the line itself has only one dimension, it's length.

I thought that's what I said in post 24:
https://www.physicsforums.com/showpost.php?p=3731892&postcount=24
and post 26:
https://www.physicsforums.com/showpost.php?p=3733530&postcount=26

 

[rustynail]

I thought that's what I said in post 24:
https://www.physicsforums.com/showpost.php?p=3731892&postcount=24
and post 26:
https://www.physicsforums.com/showpost.php?p=3733530&postcount=26

I was just putting it into my own words to know if my understanding was correct.

 

[yenchin]

I just want to ask - this is true only for cylindrical geometry, not for sphere, right?

Yes. In a sphere you will know your space is curved *intrinsically*, so again you don't have to talk about any space outside of the sphere, that's the point of intrinsic geometry.