Can an equilateral triangle have vertices at integral lattice points?
Integral lattice points are such points as (101, 254) or (3453, 12), but not points such as (123.4, 1) or (√2, 5)
If you can't find a solution in the 2D Cartesian plane, can you find one in a 3 (or more) dimensional space?
(In reply to Another way to think about it...
"and B can be on 2X,0"
Why? Doesn't this involve a loss of generality? Putting one vertex at 0,0 is OK, but the others have to be placed at arbitrary points of the integer lattice, unless you have a very good reason to do otherwise.
Posted by Richard
on 2004-06-25 13:28:49