On Centers and Central Lines of Triangles in the Elliptic Plane

Abstract

We determine barycentric coordinates of triangle centers in the elliptic plane. The main focus is put on centers that lie on lines whose euclidean limit (triangle excess --> 0) is the Euler line or the Brocard line. We also investigate curves which can serve in elliptic geometry as substitutes for the euclidean nine-point-circle, the first Lemoine circle or the apollonian circles.

29 pages / 5 figures - A conjecture of Vigara is confirmed; a contrary statement to this in the previous versions is wrong. Additionally, some minor errors are corrected and some more calculations are added. -