Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Geodesic and the shortest path

  1. Feb 18, 2010 #1
    it comes from the calculus of variation that the shortest path between two points on a surface must be geodesic.
    then must the geodesic connected two points be the shortest path?
    if not, what about the example?
    Thanks for any reply!
     
  2. jcsd
  3. Feb 19, 2010 #2
    check out the example in wikipedia
    http://en.wikipedia.org/wiki/Geodesic
     
  4. Feb 19, 2010 #3
    No. On a cylinder there are infinitely many geodesics between most points. The same is true of a flat torus.
     
  5. Feb 19, 2010 #4
    yeah, cylinder is really a good example!
     
  6. Feb 20, 2010 #5
    There is an example of a geodesic on a fluted surface of negative curvature that winds almost all of the way down the surface circling around it in a helical motion then turns around and comes back! The shortest geodesic though between two adjacent points is a simple arc. I will try to look this up. It is pretty incredible.
     
  7. Feb 21, 2010 #6
    it reminds me the magnetic lines of force in tokamak. they are all helical.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Geodesic and the shortest path
  1. Geodesic triangle (Replies: 1)

  2. Geodesic equations (Replies: 0)

  3. Geodesic problem (Replies: 3)

  4. Geodesic equation (Replies: 2)

Loading...