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?
Simple solution: The base of the triangle is paralel to the Ox axis, the triangle is rotated until it's plane reaches an angle of pi/6 with the zOx plane. The lenght of the side of the trangle is 2*n, n belongs to N.

Posted by vije
on 20040710 10:30:52 