Description
In this talk we review some theorems, problems and constructions whose proof, or study, requires tools beyond the level of “elementary geometry" in stricter sense.
To pick out an example: consider the well-known theorem which says that when reflecting the orthocentre of a triangle in each of the sides, the image points lie on the circumcircle of the triangle. What happens if we apply the same theorem on the triangle whose vertices are these new points, then we iterate this procedure in arbitrary many times? It turns out (as a conjecture, for the time being) that the iterated orthocentres are restricted within a domain that is the union of two copies of a three-cusped hypocycloid.