Kimberling Center

C. Kimberling has extensively tabulated and enumerated the properties of triangle centers (Kimberling 1994, 1998, and online), denoting the th center in his numbering scheme by . 101 (plus 13 additional) centers appeared in Kimberling (1994), 360 in Kimberling (1998), and the remainder appear in a list maintained online by Kimberling at http://faculty.evansville.edu/ck6/encyclopedia/ETC.html. In his honor, these centers are called Kimberling centers in this work. Kimberling's compilation contains 3053 centers as of December 2004. A subset of these is illustrated above.

The first few Kimberling centers are summarized in the table below with their numbers, names, and trilinears.

	center	triangle center function
	incenter	1
	triangle centroid	, ,
	circumcenter	,
	orthocenter
	nine-point center	, ,
	symmedian point	,
	Gergonne point	,
	Nagel point	,
	mittenpunkt	,
	Spieker center
	Feuerbach point	,
	harmonic conjugate of with respect to and	, ,
	first Fermat point	,
	second Fermat point	,
	first isodynamic point	,
	second isodynamic point	,
	first Napoleon point	,
	second Napoleon point	,
	Clawson point	, , ,
	de Longchamps point