Mathematica Pannonica
Volume/Issue:
Volume 28_NS2: Issue 1
Hamilton Triangle of a Triangle in the Isotropic Plane
Authors:
Zdenka Kolar-Begović Department of Mathematics, University of Osijek, Trg Ljudevita Gaja 6, Osijek, Croatia
Faculty of Education, University of Osijek, Cara Hadrijana 10, Osijek, Croatia

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and
Vladimir Volenec Department of Mathematics, University of Osijek, Trg Ljudevita Gaja 6, Osijek, Croatia
Faculty of Education, University of Osijek, Cara Hadrijana 10, Osijek, Croatia
Department of Mathematics, University of Zagreb, Bijenićka cesta 30, Zagreb, Croatia

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Pages:
1–10
Online Publication Date:
18 Feb 2022
Publication Date:
26 Apr 2022
Article Category:
Research Article
DOI:
https://doi.org/10.1556/314.2022.00001
Keywords:
standard triangle; Hamilton triangle; isotropic plane
Open access

In this paper we introduce the concept of the Hamilton triangle of a given triangle in an isotropic plane and investigate a number of important properties of this concept. We prove that the Hamilton triangle is homological with the observed triangle and with its contact and complementary triangles. We also consider some interesting statements about the relationships between the Hamilton triangle and some other significant elements of the triangle, like e.g. the Euler and the Feuerbach line, the Steiner ellipse and the tangential triangle.

  • [1]

    Beban-Brkić, J., Kolar-Šuper, R., Kolar-Begović, Z., and Volenec, V. On Feuerbach’s theorem and a pencil of circles in the isotropic plane. Journal for Geometry and Graphics 10, 2 (2006), 125–132.

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  • [2]

    Beban-Brkić, J., Kolar-Šuper, R., Kolar-Begović, Z., and Volenec, V. Gergonne’s point of a triangle in I2. Rad Hrvat. Akad. Znan. Umjet. 515, 2 (2013), 95–106.

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    Fontene, G. Correspondance. Nouv. Ann. Math. 3, 4 (1903), 183–184.

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    Guba, V. S. Zadaća no. 2049. Matematika v škole 4, (1979), 69.

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    Kolar-Begović, Z., Kolar-Šuper, R., Beban-Brkić, J., and Volenec, V. Symmedians and the symmedian center of the triangle in an isotropic plane. Mathematica Pannonica 17, 2 (2006), 287–301.

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  • [6]

    Kolar-Šuper, R., Kolar-Begović, Z., Volenec, V., and Beban-Brkić, J. Metrical relationships in a standard triangle in an isotropic plane. Mathematical Communications 10, 2 (2005), 149–157.

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  • [7]

    Kolar-Šuper, R., Kolar-Begović, Z., Volenec, V., and Beban-Brkić, J. Isogonality and inversion in an isotropic plane. International Journal of Pure and Applied Mathematics 44, 2 (2008), 339–346.

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    Pelletier, A. Problem 3440. Amer. Math. Monthly 38, (1932).

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    Sachs, H. Ebene isotrope Geometrie. Vieweg–Verlag, Braunschweig/Wiesbaden, 1987.

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    Thebault, V. Question 1963. Mathesis 14, 4 (1914), 88.

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    Thebault, V. Contributions a la géométrie du triangle. Mathesis 46, (1932), suppl. 15.

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    Volenec, V., Kolar-Begović, Z., and Kolar-Šuper, R. Steiner’s ellipses of the triangle in an isotropic plane. Mathematica Pannonica 21, 2 (2010), 229–238.

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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)

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