Glasnik Matematicki, Vol. 59, No. 2 (2024), 407-415. \( \)
EQUIDISTANT CURVE OF CONICS IN ISOTROPIC PLANE
Ema Jurkin
Faculty of Mining, Geology and Petroleum Engineering, University of Zagreb, 10 000 Zagreb, Croatia
e-mail:ema.jurkin@rgn.unizg.hr
Abstract.
In this paper we introduce the concept of equidistant curve of two curves in an isotropic plane. We study the properties of equidistant curve of conics and classify them according to their type of circularity.
2020 Mathematics Subject Classification. 51N25
Key words and phrases. Isotropic plane, conic, equidistant curve, circular curve
Full text (PDF) (access from subscribing institutions only)
https://doi.org/10.3336/gm.59.2.07
References:
-
G. Elbert and M.-S. Kim, Bisector curves of planar rational curves, Computer-Aided Design 30 (1998), 1089–1096.
-
M. Fioravanti and J. R. Sendra, Algebro-geometric analysis of bisectors of two algebraic plane curves, Comput. Aided Geom. Design 47 (2016), 189–203.
MathSciNet
CrossRef
-
E. Jurkin, Bisectors of conics in isotropic plane, Rad Hrvat. Akad. Znan. Umjet. Mat. Znan. 27(555) (2023), 175–187.
MathSciNet
CrossRef
-
E. Jurkin, Circular quartics in the isotropic plane generated by projectively linked pencils of conics, Acta Math. Hung. 130 (2011), 35–49.
MathSciNet
CrossRef
-
M. Katić Žlepalo and E. Jurkin, Equidistant sets of conic and line, in ICGG 2018 - Proceedings of the 18th International Conference on Geometry and Graphics, Cocchiarella, L. (ed.), Milan, Springer International Publishing, 2019.
-
R. Kolar-Šuper, Z. Kolar-Begović, V. Volenec and J. Beban-Brkić, Metrical relationships in a standard triangle in an isotropic plane, Math. Commun. 10 (2005), 149–157.
MathSciNet
-
M. Ponce and P. Santibáñez, On equidistant sets and generalized conics: the old and the new, Amer. Math. Monthly 121 (2014), 18–32.
CrossRef
-
H. Sachs, Ebene Isotrope Geometrie, Friedr. Vieweg & Sohn, Braunschweig, 1987.
MathSciNet
CrossRef
-
G. Salmon, A treatise on the higher plane curves: intended as a sequel to a treatise on conic sections, 3rd edition, Chelsea Publishing Company, New York, 1879.
-
J. B. Wilker, Equidistant sets and their connectivity properties, Proc. Amer. Math. Soc. 47 (1975), 449–452.
MathSciNet
CrossRef
Glasnik Matematicki Home Page