Degree of triangle centers and a generalization of the Euler line
Beiträge zur Algebra und Geometrie Volume 51 Issue 1
Page 63-89
published_at 2010
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| File | |
| Title ( eng ) |
Degree of triangle centers and a generalization of the Euler line
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| Creator | |
| Source Title |
Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometryrie
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| Volume | 51 |
| Issue | 1 |
| Start Page | 63 |
| End Page | 89 |
| Abstract |
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.
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| Keywords |
triangle center
degree of triangle center
Euler line
Nagel line
Ceva conjugate
isotomic conjugate
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| NDC |
Mathematics [ 410 ]
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| Language |
eng
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| Resource Type | journal article |
| Publisher |
Springer Verlag
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| Date of Issued | 2010 |
| Rights |
© 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
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| Publish Type | Author’s Original |
| Access Rights | open access |
| Source Identifier |
[ISSN] 0138-4821
[ISSN] 2191-0383
[NCID] AA00558880
[URI] http://eudml.org/doc/223783
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