Mathematica Pannonica
Volume/Issue:
Volume 29_NS3: Issue 1
Evolutes of Conics in the Pseudo-Euclidean Plane
Author:
Ivana Božić Dragun Civil Engineering Department, Zagreb University of Applied Sciences, Vrbik 8, Zagreb, Croatia

Search for other papers by Ivana Božić Dragun in
Current site
Google Scholar
PubMed Close
Pages:
77–86
Online Publication Date:
06 Mar 2023
Publication Date:
19 May 2023
Article Category:
Research Article
DOI:
https://doi.org/10.1556/314.2023.00006
Keywords:
Pseudo-Euclidean plane; conic; osculating circle; evolute
Open access

The evolute of a conic in the pseudo-Euclidean plane is the locus of centers of all its osculating circles. It’s a curve of order six and class four in general case. In this paper we discuss and compute the order and class of evolutes of different types of conics. We will highlight those cases that have no analogy in the Euclidean plane.

  • [1]

    BAKUROVÁ, V. On osculating pseudo-circles of curves in the pseudo-Euclidean plane. Proceedings of Symposium on Computer Geometry SCG 2011, Volume 20.

    • Search Google Scholar
    • Export Citation
  • [2]

    BAKUROVÁ, V. On Singularities of Evolutes of Curves in the Pseudo-Euclidean Plane. Proceedings of symposium on computer geometry SCG 2012, Volume 21.

    • Search Google Scholar
    • Export Citation
  • [3]

    BOŽEK, M. On Geometry of differentiable curves in the pseudo-Euclidean plane. Proceedings of Symposium on Computer Geometry SCG 2011.

  • [4]

    GLAESER, G., STACHEL, H., AND ODEHNAL, B. The Universe of conics. Springer, Berlin 2016.

  • [5]

    KOVAČEVIĆ, N. AND SZIROVICZA, V. Inversion in Minkowskischer Geometrie. Mathematica Pannonica 21/1 (2010), 89–113.

  • [6]

    KOVAČEVIĆ, N. AND JURKIN, E. Circular Cubics and Quartics in pseudo-Euclidean Plane obtained by inversion. Math. Pannon. 22(2011), 199–218.

    • Search Google Scholar
    • Export Citation
  • [7]

    SALMON, G. A Treatise on the Higher Plane Curves, Hodges, Foster, and Figgis 3d ed., Dublin 1879.

  • [8]

    SALOOM, A. AND TARI, F. Curves in the Minkowski plane and their contact with pseudo-circles. In Geom. Dedicata, Volume 159, 2012.

  • [9]

    SAVELOV, A.A. Ravninske krivulje. Školska knjiga, Zagreb, 1979;

  • [10]

    SLIEPČEVIĆ, A. AND BOŽIĆ, I. Perspective Collineation and Osculating Circle of Conic in PE-plane and I-plane. KoG 15(2011), 63–66.

    • Search Google Scholar
    • Export Citation
  • [11]

    WIELEITNER, H. Theorie der ebenen algebraischen Kurven höherer Ordnung. G. J. Göschen, Leipzig, 1905.

  • Collapse
  • Expand
Cover Mathematica Pannonica
Mathematica Pannonica
Print ISSN:
0865-2090
Online ISSN:
2786-0752

Editor in Chief: László TÓTH, University of Pécs, Pécs, Hungary

Honorary Editors in Chief:

  • † István GYŐRI, University of Pannonia, Veszprém, Hungary
  • János PINTZ, HUN-REN Alfréd Rényi Institute of Mathematics, Budapest, Hungary
  • Ferenc SCHIPP, Eötvös Loránd University, Budapest, Hungary and University of Pécs, Pécs, Hungary
  • Sándor SZABÓ, University of Pécs, Pécs, Hungary
     

Deputy Editors in Chief:

  • Erhard AICHINGER, JKU Linz, Linz, Austria
  • Ferenc HARTUNG, University of Pannonia, Veszprém, Hungary
  • Ferenc WEISZ, Eötvös Loránd University, Budapest, Hungary

Editorial Board

  • Attila BÉRCZES, University of Debrecen, Debrecen, Hungary
  • István BERKES, Rényi Institute of Mathematics, Budapest, Hungary
  • Károly BEZDEK, University of Calgary, Calgary, Canada
  • György DÓSA, University of Pannonia, Veszprém, Hungary
  • Balázs KIRÁLY – Managing Editor, University of Pécs, Pécs, Hungary
  • Vedran KRCADINAC, University of Zagreb, Zagreb, Croatia 
  • Željka MILIN ŠIPUŠ, University of Zagreb, Zagreb, Croatia
  • Gábor NYUL, University of Debrecen, Debrecen, Hungary
  • Margit PAP, University of Pécs, Pécs, Hungary
  • István PINK, University of Debrecen, Debrecen, Hungary
  • Mihály PITUK, University of Pannonia, Veszprém, Hungary
  • Lukas SPIEGELHOFER, Montanuniversität Leoben, Leoben, Austria
  • Andrea ŠVOB, University of Rijeka, Rijeka, Croatia
  • Csaba SZÁNTÓ, Babeş-Bolyai University, Cluj-Napoca, Romania
  • Jörg THUSWALDNER, Montanuniversität Leoben, Leoben, Austria
  • Zsolt TUZA, University of Pannonia, Veszprém, Hungary

Advisory Board

  • Szilárd RÉVÉSZ – Chair, HUN-REN Alfréd Rényi Institute of Mathematics, Budapest, Hungary
  • Gabriella BÖHM
  • György GÁT, University of Debrecen, Debrecen, Hungary

University of Pécs,
Faculty of Sciences,
Institute of Mathematics and Informatics
Department of Mathematics
7624 Pécs, Ifjúság útja 6., HUNGARY
(36) 72-503-600 / 4179
ltoth@gamma.ttk.pte.hu

  • Mathematical Reviews
  • Zentralblatt
  • DOAJ

Publication Model Gold Open Access
Online only
Submission Fee none
Article Processing Charge 0 EUR/article (temporarily)
Subscription Information Gold Open Access

Mathematica Pannonica
Language English
Size A4
Year of
Foundation		 1990
Volumes
per Year		 1
Issues
per Year		 2
Founder Akadémiai Kiadó
Founder's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Publisher Akadémiai Kiadó
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 2786-0752 (Online)
ISSN 0865-2090 (Print)

Monthly Content Usage

Abstract Views Full Text Views PDF Downloads
Jul 2024 0 14 0
Aug 2024 0 24 6
Sep 2024 0 75 9
Oct 2024 0 51 6
Nov 2024 0 29 5
Dec 2024 0 20 4
Jan 2025 0 13 6