Acta Scientiarum Polonorum

Currently, reflecting systems are widely used in heating equipment, solar engineering structures and acoustic
structures. Here, constructions based on classical curves do serve in reflectors. The reflection trajectories
represent such curves as podera, orthotomic and caustic paths. Research goal to find an analytical description
of the threecentred curve, its podera and orthotomics, and to build a reflecting geometric model of the existing
this arch. Such curves’ analytical description has been carried out using analytical geometry on the plane.
First, we derived podera and orthotomics formulas for a circle, and then for the threecentred arch properly.
For the geometric modeling of reflected sound waves in the threecentred arch, we selected the existing arch,
this one of the Yusupov Palace Trapeznaja Palata. The subject arch graphic representation has been build in
the AutoCAD editor, including the structure of arch properly, its podera, orthotomics and caustic for its threecentred
part. Results obtained actually affirmed the proficient acoustic phenomena knowledge appropriate to
the ancient architects capable to apply correctly in practice their skills.