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Evolutes of conics in the quasi-hyperbolic and the hyperbolic plane

izvorni znanstveni rad

izvorni znanstveni rad

Evolutes of conics in the quasi-hyperbolic and the hyperbolic plane

Vrsta prilog u časopisu
Tip izvorni znanstveni rad
Godina 2023
Časopis Journal of geometry
Volumen 114
Svesčić 2
Stranice 18, 17
DOI https://doi.org/10.1007/s00022-023-00682-6
ISSN 0047-2468
EISSN 1420-8997
Status objavljeno

Sažetak

The evolute of a conic is a curve of order six and class four in the general case. This paper is an extension of Božić Dragun (Mathematica Pannonica 29, 77–86, 2023) where we discuss and compute the order and class of evolutes of different types of conics in the pseudo-Euclidean plane. In this paper we will emphasize on the evolute’s characteristics related to Plücker formulas in the conveniently selected model of the quasi-hyperbolic plane and the projectively extended hyperbolic plane. Also construction details of the evolute of a conic in the projectively extended hyperbolic plane will be shown.

Ključne riječi

Evolute, Order, Class, Quasi-hyperbolic plane, Hyperbolic plane