1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Problem with physics points

  1. Jul 10, 2006 #1
    Given n points n1,...,nk in the xy-plane, is it always possible to find a point p such that d(ni,p) is rational for 0<i<k+1?
     
  2. jcsd
  3. Jul 10, 2006 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    What if one point is (x1,0), with x1 rational, and the other is (x2,0), with x2 irrational?
     
  4. Jul 10, 2006 #3
    Draw a line segment AB between (x1,0) and (x2,0) and a line L bisecting the line segment AB perpenticularly.
     
  5. Jul 10, 2006 #4
    um....either I'm misinterpreting the OP or the answer can be seen by drawing a circle radius p/q (where p/q is rational) around any of the points (with the point as the center).
     
  6. Jul 10, 2006 #5

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Perhaps you are misinterpreting. The question was whether, given a finite set of points, there exist a point p such that its distance to every point in the set is rational. Certainly every point on the circumference of your circle has rational distance (p/q) from the center, but what about the other points in the set?
     
  7. Jul 10, 2006 #6
    I've tried everything I know. I don't know how to produce an answer.
     
  8. Jul 10, 2006 #7

    StatusX

    User Avatar
    Homework Helper

    Was this given to you as an assignment, or did you just think of it yourself? It may be a much deeper question than it appears.
     
  9. Jul 10, 2006 #8
    A friend sent this 'funny problem' that he got from a 'funny book'. I brought it to the canadian undergraduate math conference last week and everyone was stumped.

    EDIT: Oh and d is the Euclidean metric. No cheating.
     
    Last edited: Jul 10, 2006
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Problem with physics points
  1. Fixed Point Problems (Replies: 3)

Loading...