Points from Kimberling's Encyclopedia

This master's thesis presents triangle centers described in The Encyclopedia of Triangle Centers. The first chapter introduces the encyclopedia, its author and the basic con- cepts. The second chapter summarizes the best-known triangle centers: the incenter, centroid, circumcenter, orthocenter and the nine-point center. The third chapter offers construction problems designed by the author, and the fourth chapter describes their solutions in detail. The fifth chapter focuses on the Lemoine point, symmedians, antiparal- lels and the Lemoine circles, while the sixth presents the first and second Fermat points and their properties. The seventh chapter introduces the Brocard points and discusses their connections to triangle centers. The eighth chapter offers additional construction problems, and the ninth chapter describes their solutions. The thesis also includes sections highlighting key milestones in the lives of selected mathematicians and geometers. 1