Naslov
Rose-Surfaces

Autori
Gorjanc Sonja

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

Izvornik
Abstracts, 14th Colloquium on Geometry and Graphics / Ema Jurkin, Marija Šimić - Zagreb : Hrvatsko društvo za geometriju i grafiku, 2009, 12-12

Skup
14th Colloquium on Geometry and Graphics

Mjesto i datum
Velika, Hrvatska, 06.09.2009. - 11.09.2009

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Domaća recenzija

Ključne riječi
roses; singularities of algebraic surfaces; Mathematica

Sažetak
We consider roses or rhondonea curves R(m, n) which can be expressed by polar equations $r(\varphi)=\cos\frac{;m};{;n};\, \varphi$ or $r(\varphi)=\sin\frac{;m};{;n};\, \varphi$, where $\frac{;m};{;n};$ 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(m, n) be a rose in the plane z=0. A rose-surface R(m, n, 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 $R(m, n)$ and the plane $\zeta$.}; We derive the parametric and implicit equations of R(m, n, p), visualized their shapes with the program Mathematica and investigate some of their properties such as the number and the kind of their singular lines and points.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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