Gunter Weiss
TU Vienna & TU Dresden, Wien
In 2025 P. Pech presented a special Wallace-Simson problem for quadrilaterals, namely that the four pedal points P_i with respect to a pole P form a quadrangle with parallel sides. It turns out that the locus of possible poles P is a circle. This can be proved without calculation by synthetic elementary geometric reasoning alone. Furthermore, P. Pech’s idea can be generalized to 3D-problems for tetrahedra. In addition, it gives a hint how to formulate problems generalizing the classical Wallace-Simson problem for trilaterals, too.