The Encyclopedia of Triangle Centers (ETC) is an online list of thousands of points or "
centers" associated with the geometry of a
triangle
A triangle is a polygon with three edges and three 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, any three points, when non- colline ...
. It is maintained by
Clark Kimberling, Professor of Mathematics at the
University of Evansville
The University of Evansville (UE) is a private university in Evansville, Indiana. It was founded in 1854 as Moores Hill College. The university operates a satellite center, Harlaxton College, in Grantham, England.
UE offers more than 80 differ ...
.
, 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
In geometry, the incenter of a triangle is a triangle center, a point defined for any triangle in a way that is independent of the triangle's placement or scale. The incenter may be equivalently defined as the point where the internal angle bis ...
. The information recorded about each point includes its
trilinear and
barycentric coordinates
In mathematics, an affine space is a geometric structure that generalizes some of the properties of Euclidean spaces in such a way that these are independent of the concepts of distance and measure of angles, keeping only the properties related ...
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:
:
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
The Catalogue of Triangle Cubics is an online resource containing detailed information about more than 1200 cubic curves in the plane of a reference triangle. The resource is maintained by Bernard Gilbert. Each cubic in the resource is assigned a ...
*
List of triangle topics
This list of triangle topics includes things related to the geometric shape, either abstractly, as in idealizations studied by geometers, or in triangular arrays such as Pascal's triangle or triangular matrices, or concretely in physical space. It ...
*
Triangle center
In geometry, a triangle center (or triangle centre) is a point in the plane that is in some sense a center of a triangle akin to the centers of squares and circles, that is, a point that is in the middle of the figure by some measure. For exampl ...
*''
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
In mathematics, modern triangle geometry, or new triangle geometry, is the body of knowledge relating to the properties of a triangle discovered and developed roughly since the beginning of the last quarter of the nineteenth century. Triangles and ...
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
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20th-century encyclopedias
21st-century encyclopedias