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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)

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Obviously no in 2D Geometry. | Comment 18 of 21 |

the area of equilateral triangle is (sqrt(3)/4)*( side squared)

If we place twopoints (0,0) and some (a,0) for the the third point works out to ( a/2, (sqrt(3)/2)*a) obviously we cannot eliminate the sqareroot of 3 in the third vertex coordinates. Yhe same will be applicable to 3D even I hope.

  Posted by Pemmadu Raghu Ramaiah on 2005-01-24 19:48:00
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