Clark Kimberling's ETC
 

Clark Kimberling


Clark Kimberling has created the famous Encyclopedia of Triangle Centers (ETC), available at the Web. It contains information about 3053 notable triangle points (February 2006).

Every point in the Kimberling's Encyclopedia of Triangle Centers has a number.
X(n) denotes the n-th Kimberling's Center. For the convenience of the reader, we give below the Kimberling's numbers of a few points:


Incenter = X(1)
Centroid = X(2)
Circumcenter = X(3)
Orthocenter = X(4)
Nine-point Center = X(5)
Symmedian Point = X(6)
Gergonne Point = X(7)
Nagel Point = X(8)
Mittenpunkt = X(9)
Spieker Center = X(10)
Feuerbach Point = X(11)
Second Feuerbach Point = X(12)
First Fermat Point = X(13)
Second Fermat Point = X(14)
First Isodynamic Point = X(15)
Second Isodynamic Point = X(16)
First Napoleon Point = X(17)
Second Napoleon Point = X(18)
Clawson Point = X(19)
de Longchamps Point = X(20)
Schiffler Point = X(21)
Exeter Point = X(22)
Far-out Point = X(23)
Brocard Midpoint = X(39)
Bevan Point = X(40)
Kosnita Point = X(54)
Internal Center of Similitude of Circumcircle and Incircle = X(55)
External Center of Similitude of Circumcircle and Incircle = X(56)
Third Brocard Point = X(76)
Tarry Point = X(98)
Steiner Point = X(99)
Congruent Isoscelizers Point = X(173)
Yff Center of Conguence = X(174)
Center of the Outer Soddy Circle = X(175)
Center of the Inner Soddy Circle = X(176)
First Ajima-Malfatti Point = X(179)
Apollonius Point = X(181)
Center of the Brocard circle = X(182)
Equal Parallelians Point = X(192)
Center of the Orthocentroidal circle = X(381)
Outer Eppstein Point = X(481)
Inner Eppstein Point = X(482)
Center of the Radical Circle of the Malfatti Circles = X(483)
Center of the Apollonius Circle = X(970)
First de Villiers Point = X(1127)

Centroid of the Incentral Triangle = X(1962)
Orthocenter of the Incentral Triangle = X(500)

Incenter of the Excentral Triangle = X(164)
Centroid of the Excentral Triangle = X(165)
Circumcenter of the Excentral Triangle = X(40)
Orthocenter of the Excentral Triangle = X(1)
Nine-Point Center of the Excentral Triangle = X(3)
Symmedian Point of the Excentral Triangle = X(9)
Gergonne Point of the Excentral Triangle = X(166)
Nagel Point of the Excentral Triangle = X(167)
Mittenpunkt of the Excentral Triangle = X(168)

Incenter of the Medial Triangle = X(10)
Centroid of the Medial Triangle = X(2)
Circumcenter of the Medial Triangle = X(5)
Orthocenter of the Medial Triangle = X(3)
Nine-Point Center of the Medial Triangle = X(140)
Symmedian Point of the Medial Triangle = X(141)
Gergonne Point of the Medial Triangle = X(9)
Nagel Point of the Medial Triangle = X(1)
Mittenpunkt of the Medial Triangle = X(142)
Spieker Center of the Medial Triangle = X(1125)

Incenter of the Anticomplementary Triangle = X(8)
Centroid of the Anticomplementary Triangle = X(2)
Circumcenter of the Anticomplementary Triangle = X(4)
Orthocenter of the Anticomplementary Triangle = X(20)
Nine-Point Center of the Anticomplementary Triangle = X(3)
Symmedian Point of the Anticomplementary Triangle = X(69)
Gergonne Point of the Anticomplementary Triangle = X(144)
Nagel Point of the Anticomplementary Triangle = X(145)
Mittenpunkt of the Anticomplementary Triangle = X(7)
Spieker Center of the Anticomplementary Triangle = X(1)

Centroid of the Orthic Triangle = X(51)
Circumcenter of the Orthic Triangle = X(5)
Orthocenter of the Orthic Triangle = X(52)
Nine-Point Center of the Orthic Triangle = X(143)
Symmedian Point of the Orthic Triangle = X(53)

Centroid of the Tangential Triangle = X(154)
Circumcenter of the Tangential Triangle = X(26)
Orthocenter of the Tangential Triangle = X(155)
Nine-Point Center of the Tangential Triangle = X(156)
Symmedian Point of the Tangential Triangle = X(157)

Incenter of the Intouch Triangle = X(177)
Centroid of the Intouch Triangle = X(354)
Circumcenter of the Intouch Triangle = X(1)
Orthocenter of the Intouch Triangle = X(65)
Nine-Point Center of the Intouch Triangle = X(942)
Symmedian Point of the Intouch Triangle = X(7)

Perspector of the Incentral Triangle and Excentral Triangle = X(1)
Perspector of the Incentral Triangle and Anticomplementary Triangle = X(192)
Perspector of the Incentral Triangle and Tangential Triangle = X(55)
Perspector of the Medial Triangle and Excentral Triangle = X(9)
Homothetic Center the Medial Triangle and Anticomplementary Triangle = X(2)
Perspector of the Medial Triangle and Tangential Triangle = X(3)
Perspector of the Orthic Triangle and Excentral Triangle = X(46)
Perspector of the Orthic Triangle and Anticomplementary Triangle = X(193)
Homothetic Center the Orthic Triangle and Tangential Triangle = X(25)
Perspector of the Symmedial Triangle and Excentral Triangle = X(43)
Perspector of the Symmedial Triangle and Anticomplementary Triangle = X(194)
Perspector of the Symmedial Triangle and Tangential Triangle = X(6)
Homothetic Center the Intouch Triangle and Excentral Triangle = X(57)
Perspector of the Intouch Triangle and Anticomplementary Triangle = X(145)
Perspector of the Intouch Triangle and Tangential Triangle = X(1486)
Perspector of the Extouch Triangle and Excentral Triangle = X(40)
Perspector of the Extouch Triangle and Anticomplementary Triangle = X(144)
Perspector of the Extouch Triangle and Tangential Triangle = X(197)

Perspector of Triangle ABC and Medial Triangle of the Incentral Triangle = X(37)
Perspector of Triangle ABC and Orthic Triangle of the Incentral Triangle = X(35)
Perspector of Triangle ABC and Incentral Triangle of the Medial Triangle = X(75)
Homothetic Center of Triangle ABC and Medial Triangle of the Medial Triangle = X(2)
Perspector of Triangle ABC and Orthic Triangle of the Medial Triangle = X(69)
Perspector of Triangle ABC and Symmedial Triangle of the Medial Triangle = X(76)
Perspector of Triangle ABC and Intouch Triangle of the Medial Triangle = X(8)
Perspector of Triangle ABC and Extouch Triangle of the Medial Triangle = X(7)
Perspector of Triangle ABC and Medial Triangle of the Orthic Triangle = X(6)
Perspector of Triangle ABC and Orthic Triangle of the Orthic Triangle = X(24)
Perspector of Triangle ABC and Symmedial Triangle of the Orthic Triangle = X(2052)
Perspector of Triangle ABC and Medial Triangle of the Symmedial Triangle = X(39)
Perspector of Triangle ABC and Orthic Triangle of the Symmedial Triangle = X(2056)
Perspector of Triangle ABC and Incentral Triangle of the Intouch Triangle = X(174)
Perspector of Triangle ABC and Medial Triangle of the Intouch Triangle = X(1)
Homothetic Center of Triangle ABC and Orthic Triangle of the Intouch Triangle = X(57)
Perspector of Triangle ABC and Symmedial Triangle of the Intouch Triangle = X(7)
Perspector of Triangle ABC and Intouch Triangle of the Intouch Triangle = X(173)
Perspector of Triangle ABC and Extouch Triangle of the Intouch Triangle = X(258)
Perspector of Triangle ABC and Medial Triangle of the Extouch Triangle = X(9)
Perspector of Triangle ABC and Orthic Triangle of the Extouch Triangle = X(2057)

Complement of the Incenter = X(10)
Complement of the Centroid = X(2)
Complement of the Circumcenter = X(5)
Complement of the Orthocenter = X(3)
Complement of the Nine-point Center = X(140)
Complement of the Symmedian Point = X(141)
Complement of the Gergonne Point = X(9)
Complement of the Nagel Point = X(1)
Complement of the Mittenpunkt = X(142)
Complement of the Spieker Center = X(1125)

Anticomplement of the Incenter = X(8)
Anticomplement of the Centroid = X(2)
Anticomplement of the Circumcenter = X(4)
Anticomplement of the Orthocenter = X(20)
Anticomplement of the Nine-point Center = X(3)
Anticomplement of the Symmedian Point = X(69)
Anticomplement of the Gergonne Point = X(144)
Anticomplement of the Nagel Point = X(145)
Anticomplement of the Mittenpunkt = X(7)
Anticomplement of the Spieker Center = X(1)

Isogonal Conjugate of the Incenter = X(1)
Isogonal Conjugate of the Centroid = X(6)
Isogonal Conjugate of the Circumcenter = X(4)
Isogonal Conjugate of the Orthocenter = X(3)
Isogonal Conjugate of the Nine-point Center = X(54)
Isogonal Conjugate of the Symmedian Point = X(2)
Isogonal Conjugate of the Gergonne Point = X(55)
Isogonal Conjugate of the Nagel Point = X(56)
Isogonal Conjugate of the Mittenpunkt = X(57)
Isogonal Conjugate of the Spieker Center = X(58)

Isotomic Conjugate of the Incenter = X(75)
Isotomic Conjugate of the Centroid = X(2)
Isotomic Conjugate of the Circumcenter = X(264)
Isotomic Conjugate of the Orthocenter = X(69)
Isotomic Conjugate of the Nine-point Center = X(95)
Isotomic Conjugate of the Symmedian Point = X(76)
Isotomic Conjugate of the Gergonne Point = X(8)
Isotomic Conjugate of the Nagel Point = X(7)
Isotomic Conjugate of the Mittenpunkt = X(85)
Isotomic Conjugate of the Spieker Center = X(86)

Cyclocevian Conjugate of the Incenter = X(1029)
Cyclocevian Conjugate of the Centroid = X(4)
Cyclocevian Conjugate of the Orthocenter = X(2)
Cyclocevian Conjugate of the Symmedian Point = X(1031)
Cyclocevian Conjugate of the Gergonne Point = X(7)
Cyclocevian Conjugate of the Nagel Point = X(189)

Midpoint of the Incenter and Centroid = X(551)
Midpoint of the Incenter and Circumcenter = X(1385)
Midpoint of the Incenter and Orthocenter = X(946)
Midpoint of the Centroid and Circumcenter = X(549)
Midpoint of the Centroid and Orthocenter = X(381)
Midpoint of the Circumcenter and Orthocenter = X(5)

Reflection of the Circumcenter in the Incenter = X(1482)
Reflection of the Orthocenter in the Incenter = X(944)
Reflection of the Circumcenter in the Centroid = X(381)
Reflection of the Orthocenter in the Centroid = X(376)
Reflection of the Incenter in the Circumcenter = X(40)
Reflection of the Centroid in the Circumcenter = X(376)
Reflection of the Orthocenter in the Circumcenter = X(20)
Reflection of the Circumcenter in the Orthocenter = X(382)

Inverse of the Incenter in the Circumcircle = X(36)
Inverse of the Centroid in the Circumcircle = X(23)
Inverse of the Orthocenter in the Circumcircle = X(186)
Inverse of the Nine-point Center in the Circumcircle = X(2070)
Inverse of the Symmedian Point in the Circumcircle = X(187)
Inverse of the Spieker Center in the Circumcircle = X(1324)

Internal Similitude Center of the Incircle and Circumcircle = X(55)
Internal Similitude Center of the Circumcircle and Nine-Point Circle = X(2)

External Similitude Center of the Incircle and Nine-Point Circle = X(11)
External Similitude Center of the Circumcircle and Nine-Point Circle = X(4)

Yiu Conjugate of the Incenter and Incenter = X(6)
Yiu Conjugate of the Incenter and Circumcenter = X(48)
Yiu Conjugate of the Incenter and Orthocenter = X(19)
Yiu Conjugate of the Circumcenter and Circumcenter = X(577)
Yiu Conjugate of the Circumcenter and Orthocenter = X(6)
Yiu Conjugate of the Orthocenter and Orthocenter = X(393)