Friday

December 19, 2014

December 19, 2014

Posted by **Shrek** on Thursday, April 15, 2010 at 3:57am.

m and n are integers. Let¡¦s call a point P = (x, y) ¡§generic¡¦¡¦ if all the distances from P

to lattice points are different.

With some algebraic work, I checked that the point S = ( , ) is generic.

However, the point T = (0, £k) is not generic because it is equally distant from the lattice

points (1, 0) and (-1, 0).

„½ Is there some generic point with rational coordinates?

That is, if Q = (r, s) for rational numbers r and s, must there exist two lattice points

equidistant from Q ?

As a first step, show that R = ( , ) is not generic. (Find lattice points A, B equidistant from R.)

Can you use those ideas to answer the general question?

- Algebra -
**Anonymous**, Friday, May 3, 2013 at 7:21amBut how ???

**Answer this Question**

**Related Questions**

lattice point - A lattice point is an ordered pair (x, y) where both x and y are...

Math - How many {(1,1),(1,−1),(2,0)}-lattice paths are there from the ...

sd224 - Let S be the set of {(1,0),(0,1),(1,1),(1,−1),(−1,1)}-...

help~MATHS - Let S be the set of {(1,0),(0,1),(1,1),(1,−1),(−1,1)}-...

maths - How many lattice points lie on the sphere x^2+y^2+z^2=2013? Details and ...

math - Let S be the set of {(1,1), (1,−1), (−1,1), (1,0), (0,1)}-...

math - Let S be the set of {(1,1), (1,−1), (−1,1), (1,0), (0,1)}-...

Parametric equations/Trigonometry - Lattice points - A lattice point is a point ...

Math (Combinatorics) - In the plane, the points with integer coordinates are ...

Math (Combinatorics) - In the plane, the points with integer coordinates are ...