leftri rightri

Angel Montesdeoca's Hechos Geométricos en el Triángulo (2022)

Paul Yiu's Introduction to the Geometry of the Triangle

Jean-Louis Ayme's Geometry * Géométrie * Geometria

Bernard Gibert's Cubics in the Triangle Plane

Triangle Geometry at MathWorld

Homepage Floor van Lamoen

Grinberg at MathWorld

Moses at MathWorld

Triangle Centers

Historical / Biographical

The Rise, Fall, and Possible Transfiguration of Triangle Geometry: A Mini-history, by Philip J. Davis
MacTutor History of Mathematics Archive (University of St. Andrews)
Triangle Geometers

Geometry Software: GeoGebra Classic 6

GeoGebra site for downloading free GeoGebra Classic 6
GeoGebra Manual (for GeoGebra Classic 6)

Journals that have published triangle geometry

International Journal of Computer Discovered Mathematics
Forum Geometricorum (2001-2019)
Journal for Geometry and Graphics
International Journal of Geometry
American Mathematical Monthly
Mathematics Magazine
Crux Mathematicorum
Journal of Geometry

Active Triangle Geometry Interest Group (2022)


Access to archival Hyacinthos and Advanced Plane Geometry (both extinct)

Date: Wed, 22 Dec 1999
From: "Antreas P. Hatzipolakis"
Subject: Hyacinthos Mailing List

Dear Friends,

I just created a mailing list devoted to Triangle Geometry. The name of the list is Hyacinthos (in honor of Emile Michel Hyacinthe Lemoine).

By 7 March 2013, the number of messages had passed 21,600.

FORMERLY, subscriptions were available at HYACINTHOS. Messages have been preserved and made accessible by César Lozada. Many of these have been given new links in ETC, and others can be accessed by knowing the message number and following this example:


Simply replace 25017 by the message number that is shown in ETC. The same procedure works for ADGEOM messages, starting with


Dan Reznik's Dynamic Geometry Sites

Interactive Videos and Applets (2019-2021) 6
Loci of Ellipse-Mounted Triangle Centers
Triangles and Ellipses: Pages and Media
YouTube Channel: Videos

Recent triangle geometry in International Journal of Computer Discovered Mathematics

List and access to Stanley Rabinowitz's triangle geometry articles

Euler Coordinates in the Plane of a Triangle

Algebra and Functional Equations associated with triangle geometry

Most of the articles listed here can be downloaded from sites found by searching with Google.

Major Centers of Triangles, Amer. Math. Monthly 104 (1997) 431-438.

Triangle centers as functions, Rocky Mtn. J. Math. 23 (1993) 1269-1286.

A class of major centers of triangles, Aequationes Math. 55 (1998) 251-258.

Functional equations associated with triangle geometry, Aequationes Math. 45 (1993-94) 127-152.

Collineations, conjugacies, and cubics, Forum Geometricorum 2 (2002) 21-32.

Bicentric pairs of points and related triangle centers, Forum Geometricorum 3 (2003) 35-47.

Symbolic substitutions in the transfigured plane of a triangle, Aequationes Math. 73 (2007) 156-171.

Ceva Collineations, Forum Geometricorum 9 (2007) 67-72.

Mappings associated with vertex triangles, Forum Geometricorum 9 (2009) 27-39.

A Combinatorial Classification of Triangle Centers on the Line at Infinity, J. of Integer Sequences 22 (2019) 1-13.

Polynomial triangle centers on the line at infinity, J. of Geometry 111 (2020) 1-10.

Permutation Ellipses, J. for Geometry and Graphics 24 (2020) 233-247.

Mappings from the Plane of a Triangle to a Circumconic, J. for Geometry and Graphics 45 (2020) 35-47.

Self-inverse Gemini triangles, International J. of Geometry 9 (2020) 25-39.

Line conjugates in the plane of a triangle, Aequationes Math. online, August 2022.


The clustering of triangle centers into families has been compared to constellations of stars, and this fact has prompted the naming of certain points after stars. For a list of such names with astronomical data, visit

SkyEye - (Un)Common Star Names

The Keepers of SkyEye, Lynne Marie Stockman and David Harper, wrote to the Keeper of ETC that there are two constellation names of particular interest: Triangulum and Triangulum Australe. The alpha star in Triangulum is sometimes called Mothallah. According to Richard Hinckley Allen in Star Names: Their Lore and Meaning (originally published in 1899 and then first republished by Dover in 1963), the constellation name was translated by Arab astronomers as Almutallath, Almutaleh, Almutlato, Mutlat, etc. He goes on to say that the constellation was known as Shalish to the Jews, from the name of a triangular-shaped musical instrument. The Romans knew the constellation as Deltotum, and it has had various other names over the centuries: Aegyptus, Nilus (both after the Nile delta of Egypt), Trigonum, Trigonus, etc. The alpha star in Triangulum Australe is called Atria.

Contact the Keeper

Your suggestions for improving ETC are welcome, as are submissions of new centers (and bicentric pairs) for possible inclusion in ETC. To submit such a center, send the simplest barycentric coordinates you can find, expressed as functions of sidelengths a,b,c or vertex angles A,B,C, or both. Also send, in quotable wording, geometric information about the center. Of course, before sending, you should check a search page, such as Search_13_6_9. Send to Clark Kimberling (University of Evansville)

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