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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 23 December 2018^[update], the list identifies 30,451 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.

The first 10 points listed in the Encyclopedia are:

ETC reference	Name	Definition
X(1)	incenter	center of the incircle
X(2)	centroid	intersection of the three medians
X(3)	circumcenter	center of the circumscribed circle
X(4)	orthocenter	intersection of the three altitudes
X(5)	nine-point center	center of the nine-point circle
X(6)	symmedian point	intersection of the three symmedians
X(7)	Gergonne point	symmedian point of contact triangle
X(8)	Nagel point	intersection of lines from each vertex to the corresponding semiperimeter point
X(9)	Mittenpunkt	symmedian point of the triangle formed by the centers of the three excircles
X(10)	Spieker center	center of the Spieker circle

Other points with entries in the Encyclopedia include:

ETC reference	Name
X(11)	Feuerbach point
X(13)	Fermat point
X(15), X(16)	first and second isodynamic points
X(17), X(18)	first and second Napoleon points
X(20)	de Longchamps point
X(21)	Schiffler point
X(22)	Exeter point
X(39)	Brocard midpoint

See also

• List of triangle topics


• Triangle center

References

External links

• Official website


• Weisstein, Eric W. "Kimberling Center". MathWorld..mw-parser-output cite.citationfont-style:inherit.mw-parser-output .citation qquotes:"""""""'""'".mw-parser-output .citation .cs1-lock-free abackground:url("//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png")no-repeat;background-position:right .1em center.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration abackground:url("//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Lock-gray-alt-2.svg/9px-Lock-gray-alt-2.svg.png")no-repeat;background-position:right .1em center.mw-parser-output .citation .cs1-lock-subscription abackground:url("//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Lock-red-alt-2.svg/9px-Lock-red-alt-2.svg.png")no-repeat;background-position:right .1em center.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registrationcolor:#555.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration spanborder-bottom:1px dotted;cursor:help.mw-parser-output .cs1-ws-icon abackground:url("//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/12px-Wikisource-logo.svg.png")no-repeat;background-position:right .1em center.mw-parser-output code.cs1-codecolor:inherit;background:inherit;border:inherit;padding:inherit.mw-parser-output .cs1-hidden-errordisplay:none;font-size:100%.mw-parser-output .cs1-visible-errorfont-size:100%.mw-parser-output .cs1-maintdisplay:none;color:#33aa33;margin-left:0.3em.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration,.mw-parser-output .cs1-formatfont-size:95%.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-leftpadding-left:0.2em.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-rightpadding-right:0.2em


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  Implementation of ETC points as Perl subroutines by Jason Cantarella