The pencils of curves of the third and fourth order obtained by mapping the pencils of conics

[G. D. Đukanović]

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Arhitektura i urbanizam - Geometrija arhitektonske forme / Architecture and Urbanism - Geometry of Architectural Form

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.

relativisticka geometrija, inverzija kao harmonijska simetrija, pramen krivih 3. i 4. reda, pramen povrsi 3. i 4. reda

relativistic geometry, inversion as harmonic symmetry, pencil of curves of the 3rd and 4th order, pencil of surfaces of the 3rd and 4th order

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