Naslov
Visualiztions of Rose-Surfaces

Autori
Gorjanc, Sonja

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

Izvornik
Conference on Geometry Theory and Applications Book of Abstracts / Bohumir Bastl, Miroslav Lavicka - Plzeň : Vydavatelsky servis, 2009

ISBN
978-80-86843-27-8

Skup
Conference on Geometry Theory and Applications

Mjesto i datum
Plzeň, Češka Republika, 29.06.2009. - 02.07.2009

Vrsta sudjelovanja
Poster

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
algebraic surfaces; higher singularities; roses; rose-surfaces

Sažetak
Roses or rhodonea curves $R(n, d)$ can be expressed by polar equations $r(\varphi)=\cos\frac{; ; ; m}; ; ; {; ; ; n}; ; ; \, \varphi$ or $r(\varphi)=\sin\frac{; ; ; m}; ; ; {; ; ; n}; ; ; \, \varphi$, where $\frac{; ; ; n}; ; ; {; ; ; d}; ; ; $ is a rational number in the simplest form. For such curves we construct surfaces in the following way: Let $P(0, 0, p)$ be any point on the axis $z$ and let $R(n, d)$ be a rose in the plane $z=0$. A rose-surface $\mathcal R(n, d, p)$ is the system of circles which lie in the planes $\zeta$ through the axis $z$ and have diameters $\overline{; ; ; PR_i}; ; ; $, where $R_i\neq O$ are the intersection points of the rose $R(n, d)$ and the plane $\zeta$. We derive the parametric and implicit equations of $\mathcal R(n, d, p)$, visualized their shapes with the program Mathematica and investigate some of their properties such as its order and the number and kind of their singular lines and points.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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