Lately I have become fascinated with triangle centres. To that end, I have written a small Python module that can compute explicit positions of centres for arbitrary triangles in the plane to arbitrary precision, based on the trilinear and barycentric coordinates in Kimberling's Encyclopedia of T...

In Kimberling's Encyclopedia of Triangle Centers, a lot of centres are described as the centres of certain central triangles of the reference triangle, whether as a main or alternate definition. For example, $X_{164}$ is defined as the incentre of the excentral triangle (whose vertices are the tr...