Results 1 to 2 of 2

Math Help - shortest path around cylinder

  1. #1
    Newbie
    Joined
    Jul 2008
    Posts
    19

    shortest path around cylinder

    An ant starts at a point P on the bottom edge of a right circular cylinder of radius R and height H. If the ant makes n complete circuits around the cylinder and finishes at a point at the top edge directly above its starting point, find, with justification, the length of its shortest possible path.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by scipa View Post
    An ant starts at a point P on the bottom edge of a right circular cylinder of radius R and height H. If the ant makes n complete circuits around the cylinder and finishes at a point at the top edge directly above its starting point, find, with justification, the length of its shortest possible path.
    Slit the cylinder vertically from the ants starting point and flatten out. Now take n copies of the flattened cylinder and place them side by side.

    The shortest path on the cylinder is equivalent to a diagonal on the rectangle made out of n flattened copies of the cylinder.

    RonL
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Little trick for shortest path
    Posted in the Discrete Math Forum
    Replies: 6
    Last Post: May 6th 2010, 09:37 AM
  2. Cubes, networks and shortest path.
    Posted in the Discrete Math Forum
    Replies: 9
    Last Post: April 21st 2010, 06:00 PM
  3. Yen's algorithm - shortest path - Graphs
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: November 12th 2009, 12:52 PM
  4. Shortest Path - Topology
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: March 19th 2009, 08:00 AM
  5. shortest path
    Posted in the Advanced Applied Math Forum
    Replies: 0
    Last Post: January 5th 2009, 12:03 PM

Search Tags


/mathhelpforum @mathhelpforum