# Problem with physics points

1. Jul 10, 2006

### Dragonfall

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. Jul 10, 2006

### HallsofIvy

Staff Emeritus
What if one point is (x1,0), with x1 rational, and the other is (x2,0), with x2 irrational?

3. Jul 10, 2006

### Dragonfall

Draw a line segment AB between (x1,0) and (x2,0) and a line L bisecting the line segment AB perpenticularly.

4. Jul 10, 2006

### daveb

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).

5. Jul 10, 2006

### HallsofIvy

Staff Emeritus
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?

6. Jul 10, 2006

### Dragonfall

I've tried everything I know. I don't know how to produce an answer.

7. Jul 10, 2006

### StatusX

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.

8. Jul 10, 2006

### Dragonfall

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