- John Golden
Martin Holtham has a brilliant Desmos sketch (https://www.desmos.com/calculator/ej3ubbuqfm), which got me putzing around in GeoGebra. The idea is to make the vertices of a triangle (or regular n-gon in his applet) move a portion of the time, and to trace the incenter. His loci are crazy shapes, which got me interested. Mine aren't nearly as unexpected, which is something to think about. a is the portion of time the points are moving, and C_0, D_0 and E_0 are the initial vertices of the triangle. Since this is geometric, it's easy to add the centroid as well.