World Library  
Flag as Inappropriate
Email this Article

Encyclopedia of Triangle Centers

Article Id: WHEBN0015003593
Reproduction Date:

Title: Encyclopedia of Triangle Centers  
Author: World Heritage Encyclopedia
Language: English
Subject: Clark Kimberling
Publisher: World Heritage Encyclopedia

Encyclopedia of Triangle Centers

The Encyclopedia of Triangle Centers (ETC) is an online list of more than 6,000 points or "centers" associated with the geometry of a triangle. It is maintained by Clark Kimberling, Professor of Mathematics at the University of Evansville.

As of 6 June 2015, the list identifies 7,691 triangle centers.[1]

Each point in the list is identified by an index number of the form X(n)—for example, X(1) is the incenter. The information recorded about each point includes its trilinear and barycentric coordinates and its relation to lines joining other identified points. Links to The Geometer's Sketchpad diagrams are provided for key points. The Encyclopedia also includes a glossary of terms and definitions.

Each point in the list is assigned a unique name. In cases where no particular name arises from geometrical or historical considerations, the name of a star is used instead. For example the 770th point in the list, is named point Acamar.

The first 10 points listed in the Encyclopedia are:

ETC reference Name Definition
X(1) incenter center of the incircle
X(2) centroid intersection of the three medians
X(3) circumcenter center of the circumscribed circle
X(4) orthocenter intersection of the three altitudes
X(5) nine-point center center of the nine-point circle
X(6) symmedian point intersection of the three symmedians
X(7) Gergonne point symmedian point of contact triangle
X(8) Nagel point intersection of lines from each vertex to the corresponding semiperimeter point
X(9) Mittenpunkt symmedian point of the triangle formed by the centers of the three excircles
X(10) Spieker center center of the Spieker circle

Other points with entries in the Encyclopedia include:

ETC reference Name
X(11) Feuerbach point
X(13) Fermat point
X(15), X(16) first and second isodynamic points
X(17), X(18) first and second Napoleon points
X(20) de Longchamps point
X(21) Schiffler point
X(39) Brocard midpoint

See also


  1. ^ Centers X(7001) -

External links

  • Encyclopedia of Triangle Centers
  • Weisstein, Eric W., "Kimberling Center", MathWorld.
  • Implementation of ETC points as Perl subroutines by Jason Cantarella
This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.

Copyright © World Library Foundation. All rights reserved. eBooks from Project Gutenberg are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.