Pramenovi krivih trećeg i četvrtog reda dobijeni preslikavanjem pramenova konika
The pencils of curves of the third and fourth order obtained by mapping the pencils of conics
Abstract
Harmonijskom simetrijom, kao potpuno bijektivnom i
konformnom centralnom inverzijom, prikazana je
transformacija svih tipova pramenova konika i njihovih
specifičnosti u pramenove krivih trećeg i četvrtog reda i
njihove preslikane specifičnosti, i obrnuto.
Prepoznavanjem ekvivalentnosti inverzije sa klasičnom
osnom simetrijom (nekomformna simetrija) ukazano je
na neograničene mogućnosti za preslikavanje krivih i
površi i dobijanje novih oblika koji će biti od koristi i u
teoriji geometrije kao i u arhitektonskoj praksi
Harmonic symmetry, which is a completely bijective
and conformal central inversion, is used to present
the transformation of all types of pencils of conics and
their specific features into the pencils of curves
of the 3rd and 4th order and their mapped specific
features and vice versa. The recognition of the
equivalence of inversion with the classical axial
symmetry (non-conformal symmetry) has created
numerous possibilities for mapping curves and surfaces
and obtaining new forms which can be of great use both
in the theory of geometry and in the practice of architecture.