18 Nov
2011
18 Nov
'11
9:03 a.m.
I also point out that (assuming Reid proof valid) by combining my Buchholz-->nonprimitive coordinates formula, and the Gaussian GCD, we can actually write just a single formula in terms of n,m,k, rational operations, and Gaussian GCD, giving coordinates for every PRIMITIVE Heronian triangle's vertices A,B,C. That is quite cool. Here are the nonprimitive coordinate formulas: xC = m*(n-k)*(n+k); yC = 2*k*m*n; xA = n*(m-k)*(m+k) + xC; yA = 0; xB = 0; yB = 0; and now the primitivization as Gaussian integers is 0, xA/G, and (xC+yC*i)/G where G=GaussianGCD(xA, xC+yC*i).