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?
http://mathforum.org/library/drmath/view/61862.html
has a proof somewhat similar to Tristan's but not nearly as nice as his in my opinion.
You get a number of other references such as
http://recpuzzles.org/new/sol.pl/geometry/lattice/equilateral
if you google equilateral lattice triangle.
Edited on June 21, 2004, 12:16 am

Posted by Richard
on 20040620 19:53:33 