Geodesic Deviation on an Infinite Cylinder

[rbwang1225]

Homework Statement

Ants follow geodesics on a surface which is an infinite cylinder.
Do the geodesics deviate?
By considering only the paths of itself and its neighbors, can an ant decide whether it is on a cylinder of a plane?

The Attempt at a Solution

My answer to the first question is no, since the geodesic on the cylinder is a straight line(?).
For the second question, my answer is also no, since they do not approach together or depart from each other.
I just don't know my answers are right or wrong.
Any comment would be appreciated.

 

[anathema]

Your answers are partially correct. Yes, the geodesics on a cylinder are straight lines, so they do not deviate. However, the second question is a bit more complex. While ants may not be able to determine whether they are on a cylinder or a plane based on their own paths and those of their neighbors, they may be able to do so by observing other factors such as the curvature of the surface or the behavior of other ants on the surface. Additionally, if the ants were able to move in a three-dimensional space, they may be able to detect the curvature of the surface by observing their own movements. So, the answer to the second question may not be a definitive "no". It would depend on the abilities and observations of the ants in question. I hope this helps clarify your understanding. Keep exploring and questioning!