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  |  ,
 ,
![bc[a^2b^2+a^2c^2-(b^2-c^2)^2]](https://txtdot.deep-swarm.xyz/proxy/img?url=https%3A%2F%2Fmathworld.wolfram.com%2Fimages%2Fequations%2FKimberlingCenter%2FInline23.svg){kind=small} |
 | 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  |  |
See also
Major Triangle Center, Triangle Center, Triangle Center Function
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References
Kimberling, C. "Central Points and Central Lines in the Plane of a Triangle." Math. Mag. 67, 163-167, 1994.Kimberling, C. "Triangle Centers and Central Triangles." Congr. Numer. 129, 1-295, 1998.Kimberling, C. "Clark Kimberling's Encyclopedia of Triangle Centers--ETC." http://faculty.evansville.edu/ck6/encyclopedia/ETC.html.Kimberling, C. "Encyclopedia of Triangle Centers." http://faculty.evansville.edu/ck6/encyclopedia/.Kimberling, C. "Triangle Centers." http://faculty.evansville.edu/ck6/tcenters/.Pegg, E. Jr. and Weisstein, E. W. "Seven Mathematical Tidbits." MathWorld Headline News. Nov. 8, 2004. http://mathworld.wolfram.com/news/2004-11-08/seventidbits/#3.
Referenced on Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Kimberling Center." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/KimberlingCenter.html