Degree of triangle centers and a generalization of the Euler line
degree of triangle center
We introduce a concept “degree of triangle centers", and give a formula expressing the degree of triangle centers on generalized Euler lines. This generalizes the well known 2 : 1 point configuration on the Euler line. We also introduce a natural family of triangle centers based on the Ceva conjugate and the isotomic conjugate. This family contains many famous triangle centers, and we conjecture that the degree of triangle centers in this family always takes the form (-2)k for some k ∈ Z.
Contributions to Algebra and Geometryrie
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© 2010 Heldermann Verlag
This is a post-peer-review, pre-copyedit version of an article published in Beiträge zur Algebra und Geometrie. The final authenticated version is available online at: http://eudml.org/doc/223783
Graduate School of Science