Anthony Manning(Mathematics Institute, University of Warwick)
A map of the tetrahedron that represents taking the pedal
triangle.
Abstract:
The feet of the altitudes of a triangle are the vertices of a new
triangle called its pedal triangle. But what happens if we take the
pedal triangle of that, and repeat the process indefinitely?
We shall describe an expanding map of the tetrahedron whose orbits
represent the angles of each triangle in such a pedal sequence. If
the angles of the original triangle are an integer number of degrees
then the sequence is periodic; but, typically, the pedal sequence goes
through all possible shapes and is only acute one quarter of the time!
P. S. A síkbeli problémával Lax
Péter is foglalkozott.