Heronian Triangle Table
             Reduced integer triangles with integer areas
     14 Sep 1997 by Michael Somos <somos@grail.cba.csuohio.edu>
           http://grail.cba.csuohio.edu/~somos/tritab.txt

        Side lengths are a1,a2,a3. Angle measures are A1,A2,A3.
        tan(A1/2) = p1/q1, tan(A2/2) = p2/q2, tan(A3/2) = p3/q3.
        0 < a1 <= a2 <= a3. Vertices are (x1,y1),(x2,y2),(x3,y3).
        P = a1+a2+a3, s = P/2, s1 = s-a1, s2 = s-a2, s3 = s-a3.
        Area D = sqrt(s*s1*s2*s3).  at = 1, 2, or 3, i^2 = -1.
        q1+p1*i=(m2-n2*i)*(m3+n3*i)*i^(at==1).
        q2+p2*i=(m3-n3*i)*(m1+n1*i)*i^(at==2).
        q3+p3*i=(m1-n1*i)*(m2+n2*i)*i^(at==3).
        if at==1 then n3/m3 < n1/m1 < n2/m2.
        if at==2 then n1/m1 < n2/m2 < n3/m3.
        if at==3 then n2/m2 < n3/m3 < n1/m1.

   n  a1  a2  a3 :   P     D    x1  y1  x2  y2  x3  y3 : n1 m1 n2 m2 n3 m3 : at
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   1   3   4   5 :  12     6 :   3   0   0   4   3   4 :  0  1  1  1  2  1 : 2
   2   5   5   6 :  16    12 :   0   4   6   4   3   0 :  1  2  2  1  0  1 : 1
   3   5   5   8 :  18    12 :   3   8   3   0   0   4 :  2  1  1  2  1  1 : 3
   4   5  12  13 :  30    30 :   5   0   0  12   5  12 :  0  1  1  1  3  2 : 2
   5  10  13  13 :  36    60 :   5   0   0  12  10  12 :  0  1  2  3  3  2 : 2
   6   4  13  15 :  32    24 :   9   0   0  12   4  12 :  0  1  3  2  2  1 : 2
   7  13  14  15 :  42    84 :  14  12   5   0   0  12 :  3  2  0  1  1  2 : 3
   8   9  10  17 :  36    36 :  15   0   0   8   9   8 :  0  1  2  1  4  1 : 2
   9   8  15  17 :  40    60 :  15   8   0   0   0   8 :  1  1  0  1  1  4 : 3
  entire 79396 byte table
  The "C" program to produce it
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Last Updated Web Aug 22 15:27 EDT 2007
Michael Somos <somos@grail.cba.csuohio.edu>
WWW URL: "http://grail.cba.csuohio.edu/~somos/"