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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.)
re: Obviously no in 2D Geometry. | Comment 19 of 21 |
(In reply to Obviously no in 2D Geometry. by Pemmadu Raghu Ramaiah)

What if you placed one at (0,0) and another at (a,b)?  Then could you find an appropriate third point?  The the edge length of the triangle would not be an integer.

Please read some earlier posts.  While you may be right, I don't think your "proof" is complete.

Be very careful when using the word "obviously" =)

  Posted by nikki on 2005-01-24 20:35:52
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