Thébault’s Pencil of Circles in an Isotropic Plane

Authors

  • Vladimir Volenec Department of Mathematics, University of Zagreb, Zagreb, Croatia
  • Zdenka Kolar-Begović Department of Mathematics, University of Osijek, Osijek, Croatia
  • RužicA Kolar-Šuper Faculty of Teacher Education, University of Osijek, Osijek, Croatia

DOI:

https://doi.org/10.5644/SJM.06.2.08

Abstract

In the Euclidean plane Griffiths's and Thébault's pencil of the circles are generally different. In this paper it is shown that in an isotropic plane the pencils of circles, corresponding to the Griffiths's and Thébault's pencil of circles in the Euclidean plane, coincide.

 

2000 Mathematics Subject Classification. 51N25

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References

J. Beban-Brki´c, R. Kolar-Super, Z. Kolar-Begovi´c, V. Volenec, ˇ On Feuerbach’s theorem and a pencil of circles in the isotropic Plane, J. Geom. Graph., 10 (2) (2006), 125–132.

Z. Kolar-Begovi´c, R. Kolar-Super and V. Volenec, ˇ Angle bisectors of a triangle in I2, Math. Commun., 13 (1) (2008), 97–105.

R. Kolar-Super, Z. Kolar-Begovi´c, V. Volenec and J. Beban-Brki´c, ˇ Metrical relationships in a standard triangle in an isotropic plane, Math. Commun., 10 (2) (2005), 149–157.

R. Kolar-Super, Z. Kolar-Begovi´c and V. Volenec, ˇ Apollonius circles of the triangle in an isotropic plane, Taiwanese J. Math., 12 (5) (2008), 1239–1249.

R. A. Johnson, Advanced Euclidean Geometry, Dover, New York, 1960.

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

K. Strubecker, Geometrie in einer isotropen ebene, Math. Naturwiss. Unterricht, 15 (1962), 297-306, 343-351, 385-394.

V. Th´ebault, Sur les bissectrices du triangle, Mathesis, 46 (1932), 366–367.

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Published

11.06.2024

How to Cite

Volenec, V., Kolar-Begović, Z., & Kolar-Šuper, R. (2024). Thébault’s Pencil of Circles in an Isotropic Plane. Sarajevo Journal of Mathematics, 6(2), 237–239. https://doi.org/10.5644/SJM.06.2.08

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