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The Encyclopedia of Triangle Centers (ETC) is an online list of thousands of 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 February 2024[update], the list identifies over 61,000 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.
^Kimberling, Clark. "Part 31: Centers X(52001) - X(54000)". Encyclopedia of Triangle Centers. Retrieved February 6, 2024.
and 25 Related for: Encyclopedia of Triangle Centers information
The EncyclopediaofTriangleCenters (ETC) is an online list of thousands of points or "centers" associated with the geometry of a triangle. It is maintained...
to qualify as trianglecenters. For an equilateral triangle, all trianglecenters coincide at its centroid. However the trianglecenters generally take...
listed center, X(1), in Clark Kimberling's EncyclopediaofTriangleCenters, and the identity element of the multiplicative group oftrianglecenters. For...
form, the EncyclopediaofTriangleCenters, this list comprises tens of thousands of entries. He has contributed to The Hymn, the journal of the Hymn Society...
cubic is the locus of a point X* is on the line NX, where N is the nine-point center, (N = X(5) in the EncyclopediaofTriangleCenters). The Napoleon–Feuerbach...
p. 65) Kay (1969, p. 184) Clark Kimberling's EncyclopediaofTriangles "EncyclopediaofTriangleCenters". Archived from the original on 2012-04-19. Retrieved...
incircle is a trianglecenter called the triangle's incenter. An excircle or escribed circle of the triangle is a circle lying outside the triangle, tangent...
the triangle. It is listed as X(11) in Clark Kimberling's EncyclopediaofTriangleCenters, and is named after Karl Wilhelm Feuerbach. Feuerbach's theorem...
(and often inside) a triangle, satisfying some unique property: see the article EncyclopediaofTriangleCenters for a catalogue of them. Often they are...
Kimberling of an encyclopediaoftrianglecenters containing a listing of nearly 50,000 trianglecenters and their properties and also the compilation of a catalogue...
of similitude of the incircle and circumcircle. The Online EncyclopediaofTriangleCenters lists this point as X(56). It is defined by trilinear coordinates:...
X(13) in the EncyclopediaofTriangleCenters Archived April 19, 2012, at the Wayback Machine Entry X(14) in the EncyclopediaofTriangleCenters Archived...
Morley center ) is designated as X(356) in Clark Kimberling's EncyclopediaofTriangleCenters, while the other point called second Morley center (or the...
the guidance of Clark Kimberling, an electronic encyclopediaoftrianglecenters (ETC) has been developed, it contains more than 7000 centers and many properties...
jewels of modern geometry". In the EncyclopediaofTriangleCenters the symmedian point appears as the sixth point, X(6). For a non-equilateral triangle, it...
Spieker. The Spieker center is a trianglecenter and it is listed as the point X(10) in Clark Kimberling's EncyclopediaofTriangleCenters. The following result...
Electrothermal-chemical technology, in artillery EncyclopediaofTriangleCenters, an online list of points of a triangle Ericsson Texture Compression, an image...
associated with a plane triangle. It is a trianglecenter and is designated as X(22) in Clark Kimberling's EncyclopediaofTriangleCenters. This was discovered...
{2}+a^{2}):c(a^{2}+b^{2}),} and is a trianglecenter; it is center X(39) in the EncyclopediaofTriangleCenters. The third Brocard point, given in trilinear...
Kimberling, Clark. "Part I: Introduction and Centers X(1) – X(1000)". EncyclopediaofTriangleCenters. The circumcenter is listed under X(3). Weisstein...
Mathematical Monthly. It is denoted X(19) in Clark Kimberling's EncyclopediaofTriangleCenters. There are at least two ways to construct the Clawson point...
is a list of well-known online encyclopedias that are accessible or formerly accessible on the Internet. The largest online encyclopedias are general...
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