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?
the area of equilateral triangle is (sqrt(3)/4)*( side squared)
If we place twopoints (0,0) and some (a,0) for the the third point works out to ( a/2, (sqrt(3)/2)*a) obviously we cannot eliminate the sqareroot of 3 in the third vertex coordinates. Yhe same will be applicable to 3D even I hope.