Publikace na Matematicko-fyzikální fakulta |
2018
Abstrakt
In the contribution, the constructions of a harmonic conjugate on a line and the pole of a triangle with respect to a line are generalized into the three-dimensional analogy. As well as we use hyperspaces for the less dimensional examples, we can conveniently use the 4-space for the case in the 3-space.
The pole is constructed synthetically in the language of incidence projective geometry, and the steps of the four-dimensional construction are visualized in the framework of double orthogonal projection of the 4-space onto two mutually perpendicular 3-spaces. The construction is supported with an online interactive 3D GeoGebra model.