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?

I suspect intuitively that it's not possible in 2-D; but that it is possible in 3-D.   I'm thinking that if you imaging rotating the triangle in the third plane, say, 30 degrees, then you might get some sqrt(3) terms cancelling out.

Posted by Larry on 2004-06-20 13:24:48