Find an equilateral triangle such that the coordinates (x,y) of each vertex is an integer.

Question

jamesj · Answer

hmm. P1 = (x1,y1), P2 = (x2, y2), P3 = (x3, y3), all integral and

S1 =P2 - P1, S2 = P3 - P1, S3 = P3 - P2 such that

for all k not j
Sk.Sj = ||Sk|| ||Sj|| / 2, as cos(pi/3) = 1/2

hero · Answer

So what are the coordinates? I have no idea what you just wrote

hero · Answer

I do, but i need actual coordinates

jamesj · Answer

I just wrote down a more analytical statement of your problem.  No insight yet.  Just thinking outloud.

hero · Answer

Okay

jamesj · Answer

I'll think about it.

hero · Answer

You might want to consider utilizing some basic geometry for this.

anonymous · Answer

hey hero can u help me with a tough question?

anonymous · Answer

Look at the graph above and comment on the sign of the discriminant. Form the quadratic equation based on the information provided and find its solutions.

anonymous · Answer

see this http://www.mathpages.com/home/kmath261.htm