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 |