perplexus.info :: Geometry : Equilateral Triangle

Equilateral Triangle (Posted on 2004-06-20)

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: Another way to think about it...

| Comment 12 of 22 |

(In reply to Another way to think about it... by Gromit)

"and B can be on 2X,0"

Why? Doesn't this involve a loss of generality? Putting one vertex at 0,0 is OK, but the others have to be placed at arbitrary points of the integer lattice, unless you have a very good reason to do otherwise.

Posted by Richard on 2004-06-25 13:28:49

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