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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

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2012
Disertacija.pdf (7.901Mb)
Author
Đukanović, Gordana D.
Mentor
Petruševski, Ljiljana
Committee members
Đorđević, Đorđe
Štulić, Radovan
Obradović, Marija
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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.
Faculty:
Универзитет у Београду, Архитектонски факултет
Date:
02-11-2012
Projects:
  • New bioecological materials for soil and water protection (RS-37002)
Keywords:
relativisticka geometrija / relativistic geometry / inverzija kao harmonijska simetrija / pramen krivih 3. i 4. reda / pramen povrsi 3. i 4. reda / inversion as harmonic symmetry / pencil of curves of the 3rd and 4th order / pencil of surfaces of the 3rd and 4th order

DOI: 10.2298/bg20121102djukanovic

[ Google Scholar ]
Handle
https://hdl.handle.net/21.15107/rcub_nardus_1990
URI
https://nardus.mpn.gov.rs/handle/123456789/1990
http://eteze.bg.ac.rs/application/showtheses?thesesId=398
https://fedorabg.bg.ac.rs/fedora/get/o:6102/bdef:Content/download
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