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
re(2): short answers to a short q. by Ady TZIDON)
(0;0;0)(2a;0;0)(a;a;2*a) does not have sides of equal length.
Also, proving that it can't be done in 2D cannot be dismissed so lightly. That the square root of 3 is irrational certainly does not by itself prove the result; a lot more work is needed like what Tristan gave below. In fact, the sides of the 3D equilateral triangle with vertices (1,0,0), (0,1,0), (0,0,1) all have the irrational length of square root 2.
Edited on June 22, 2004, 1:37 pm

Posted by Richard
on 20040622 13:04:33 