Triangle Centers and Extraversions<br><br>                                                                                                             
                                                                                                                                               
I will present some interesting aspects of familiar "centers" from                                                                             
middle school geometry -- centroid, incenter, circumcenter, etc. In                                                                            
particular, I will introduce homogeneous barycentric coordinate                                                                                
system, and show how it helps illustrate the algebraic aspect of                                                                               
certain triangle centers. In the end, I'll give a definition of                                                                                
center for higher dimensions. No prior knowledge but simple plane                                                                              
geometry is required.