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.)

3D	\| Comment 13 of 22 \|

Simple solution: The base of the triangle is paralel to the Ox axis, the triangle is rotated until it's plane reaches an angle of pi/6 with the zOx plane. The lenght of the side of the trangle is 2*n, n belongs to N.

Posted by vije on 2004-07-10 10:30:52

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