On Centers and Central Lines of Triangles in the Elliptic Plane
Metric Geometry
2018-01-24 v3
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.
Keywords
Cite
@article{arxiv.1705.06187,
title = {On Centers and Central Lines of Triangles in the Elliptic Plane},
author = {Manfred Evers},
journal= {arXiv preprint arXiv:1705.06187},
year = {2018}
}
Comments
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. -