The Encyclopedia of Triangle Centers (ETC) is an online list of thousands of points or "
centers
Center or centre may refer to:
Mathematics
* Center (geometry), the middle of an object
* Center (algebra), used in various contexts
** Center (group theory)
** Center (ring theory)
* Graph center, the set of all vertices of minimum eccentrici ...
" associated with the geometry of a
triangle
A triangle is a polygon with three Edge (geometry), edges and three Vertex (geometry), vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \triangle ABC.
In Euclidean geometry, an ...
. It is maintained by
Clark Kimberling
Clark Kimberling (born November 7, 1942 in Hinsdale, Illinois) is a mathematician, musician, and composer. He has been a mathematics professor since 1970 at the University of Evansville. His research interests include triangle centers, integer seq ...
, Professor of Mathematics at the
University of Evansville.
, the list identifies 52,440 triangle centers.
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
The Geometer's Sketchpad is a commercial interactive geometry software program for exploring Euclidean geometry, algebra, calculus, and other areas of mathematics. It was created as part of the NSF-funded Visual Geometry Project led by Eugene Klo ...
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
Theta Eridani, Latinized from θ Eridani, is a binary system in the constellation of Eridanus with a combined apparent magnitude of 2.88. Its two components are designated θ1 Eridani, formally named Acamar (the traditional name of th ...
''.
The first 10 points listed in the Encyclopedia are:
:
Other points with entries in the Encyclopedia include:
:
Similar, albeit shorter, lists exist for quadri-figures (quadrilaterals and systems of four lines) and polygon geometry. (See external links)
See also
*
Catalogue of Triangle Cubics
*
List of triangle topics
*
Triangle center
*''
The Secrets of Triangles
''The Secrets of Triangles: A Mathematical Journey'' is a popular mathematics book on the geometry of triangles. It was written by Alfred S. Posamentier and , and published in 2012 by Prometheus Books.
Topics
The book consists of ten chapters, ...
''
*
Modern triangle geometry
References
External links
*
*{{MathWorld, urlname=KimberlingCenter , title=Kimberling Center
Implementation of ETC points as Perl subroutinesby Jason Cantarella
Encyclopedia of Quadri-figuresEncyclopedia of Polygon Geometry
Triangle centers
Mathematical databases
20th-century encyclopedias
21st-century encyclopedias