Naslov
Krivulje fokusa u pramenovima konika u pseudo-euklidskoj ravnini
(Curve of Foci of Pencil of Conics in Pseudo-Euclidean Plane)

Autori
Sliepčević, Ana

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

Skup
14th Scientific-Professional Collokuium on Geometry and Graphics

Mjesto i datum
Velika, Hrvatska, 06.09.2009. - 10.09.2009

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Domaća recenzija

Ključne riječi
fokus algebarske krivulje; pseudo-euklidska ravnina; pramen konika
(focus of an algebraic curve; pseudo-Euclidean plane; pencils of conics)

Sažetak
A focus of an algebraic curve in the Euclidean plane is defined as an intersection of the isotropic tangents of the curve. The curve of class m has m2 foci. An analogous definition is valid in the Pseudo-Euclidean plane. The pencils of point conics and line conics are studied on a model of PE-plane. Their curves of foci are constructed. It is shown that the curve of foci of the pencil of point conics is of order six. It has different degrees of circularity depending on the type of the pencil. It can be entirely circular as well. Some special cases that are not possible in the Euclidean plane are pointed out. The curve of foci of the pencil of line conics is circular cubic. It can happen to be entirely circular, which is not possible in the Euclidean case. Besides the curves of foci, for the same pencils of conics the curves of centers are constructed as well.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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