Dual Feuerbach Theorem in an Isotropic Plane

Ružica  Kolar-Šuper; Zdenka Kolar-Begović; Vladimir Volenec

doi:10.5644/SJM.06.1.09

Authors

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

DOI:

https://doi.org/10.5644/SJM.06.1.09

Abstract

The dual Feuerbach theorem for an allowable triangle in an isotropic plane is proved analytically by means of the so-called standard triangle. A number of statements about relationships between some concepts of the triangle and their dual concepts are also proved.

2000 Mathematics Subject Classification. 51N25

Statistics

Abstract: 38 / PDF: 12

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.

I. M. Jaglom, Reletivity Principle of Galilean and Non-Euclidean Geometry [in Russian], Nauka, Moskva 1969.

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.

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

K. Strubecker, Geometrie in einer isotropen Ebene, Math. Naturwiss. Unterr., 15 (1962), 297–306, 343–351, 385–394.