Sorry. The formula should read R = -ia'bc/(4 Area). In this case, R _is_ the (complex) vector to find O from A (A is the vertex opposite side a). For example, if A=1,0, B=2,0, C=1,1, then a=C-B=-1,1, b=A-C=0,-1, c=B-A=1,0. Then, Area = 1/2, so we get: -i*(-1-i)*(0-i)*(1+0i)/(4*1/2) = -i*(-1-i)*(-i)/2 = -1*(-1-i)/2 = (1+i)/2 A+(1+i)/2 = (1+0i)+(1+i)/2 = 3/2+i/2, which is the circumcenter of triangle ABC. My formula is easy to remember, since 1) complex multiplication is commutative; and 2) the prime tells you which vertex you're using to base the "R" vector. At 02:06 AM 6/8/2012, Adam P. Goucher wrote:
My formula is: R = -ia'bc/(4 A) where i=sqrt(-1), and a' is conjugate(a).
The left hand side should be the position vector of A with respect to O, not R. (They are only equal when this vector is real.) Your webpage is correct, however.
Sincerely,
Adam P. Goucher