In geometry, a triangle center is a point that can be called the middle of a triangle. There are many ways of measuring the center of a triangle, and each has a different name. On an equilateral triangle, every triangle center is the same, but on other triangles, the centers are different. Triangle centers may be inside or outside the triangle. Ancient Greek mathematicians discovered four: the centroid, circumcenter, incenter, and orthocenter. Today, mathematicians have discovered over 40,000 triangle centers. They are listed in the Encyclopedia of Triangle Centers, which is run by Clark Kimberling at the University of Evansville. 