Naslov
Generalized Rose-Surfaces

Autori
Gorjanc, Sonja

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
GeoGra 2012 Conference, Budapest, 20-21/01/2012 / - , 2012

Skup
GeoGra 2012 Conference

Mjesto i datum
Budimpešta, Mađarska, 20.01.2012. - 21.01.2012

Vrsta sudjelovanja
Pozvano predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
congruence of circles; circular surfaces; rose-surfaces

Sažetak
In [1] we studied circular surfaces CS($\alpha$, p)that are defined by a curve $\alpha$ and a congruence of circles C(p), where C(p) contains all circles passing through the points P(0, 0, +-p), p=$\sqrt{;q};$, $q\in\R$. Depending on the type of points P, C(p) is an elliptic, parabolic or hyperbolic congruence of circles. It was shown that the rose surfaces, treated in [2], are circular surfaces CS($\alpha$, p) where $\alpha$ is a rose (rhodonea) and C(p) is an elliptic or parabolic congurence. The rose lies in the plane z=p having the directing point P as the point of the highest multiplicity. If we extend $\alpha$ to all cyclic-harmonic curves with the polar equation, and include hyperbolic congruences C(p), numerous forms of new class of surfaces are obtained. This class we call generalized rose surfaces, study their algebraic properties and visulaize their shapes with the program Mathematica.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA