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Equilateral Triangle (Posted on 2004-06-20) Difficulty: 4 of 5
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?

No Solution Yet Submitted by SilverKnight    
Rating: 2.6000 (5 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Reference | Comment 6 of 21 |

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://rec-puzzles.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 2004-06-20 19:53:33

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