World Library  
Flag as Inappropriate
Email this Article

Splitter (geometry)

Article Id: WHEBN0014961391
Reproduction Date:

Title: Splitter (geometry)  
Author: World Heritage Encyclopedia
Language: English
Subject: Bisection, Incircle and excircles of a triangle, Semiperimeter, Concurrent lines, Collinearity, Splitter, Nagel point, List of triangle topics, Cleaver (geometry)
Collection:
Publisher: World Heritage Encyclopedia
Publication
Date:
 

Splitter (geometry)

The Nagel point (blue, N) of a triangle (black). The red triangle is the extouch triangle, and the orange circles are the excircles. The splitters of the perimeter are ATA, BTB, and CTC.

In plane geometry, a splitter is a line segment through one of the vertices of a triangle (that is, a cevian) that bisects the perimeter of the triangle.[1][2]

The opposite endpoint of a splitter to the chosen triangle vertex lies at the point on the triangle's side where one of the excircles of the triangle is tangent to that side.[1][2] This point is also called a splitting point of the triangle.[2] It is additionally a vertex of the extouch triangle and one of the points where the Mandart inellipse is tangent to the triangle side.[3]

The three splitters concur at the Nagel point of the triangle,[1] which is also called its splitting center.[2]

Some authors have used the term "splitter" in a more general sense, for any line segment that bisects the perimeter of the triangle. Other line segments of this type include the cleavers, which are perimeter-bisecting segments that pass through the midpoint of a triangle side, and the equalizers, segments that bisect both the area and perimeter of a triangle.[4]

References

  1. ^ a b c Honsberger, Ross (1995), "Chapter 1: Cleavers and Splitters", Episodes in Nineteenth and Twentieth Century Euclidean Geometry, Mathematical Association of America, pp. 1–14 .
  2. ^ a b c d Avishalom, Dov (1963), "The perimetric bisection of triangles", Mathematics Magazine 36 (1): 60–62, JSTOR 2688140, MR 1571272 .
  3. ^ Juhász, Imre (2012), "Control point based representation of inellipses of triangles", Annales Mathematicae et Informaticae 40: 37–46, MR 3005114 .
  4. ^ Kodokostas, Dimitrios (2010), "Triangle equalizers", Mathematics Magazine 83 (2): 141–146, doi:10.4169/002557010X482916 .

External links


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 USA.gov, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for USA.gov 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.