In this paper, we consider the Feuerbach point and the Feuerbach line of a triangle in the isotropic plane, and investigate some properties of these concepts and their relationships with other elements of a triangle in the isotropic plane. We also compare these relationships in Euclidean and isotropic cases.
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. J. Geom. Graph. (2006), 125–132.
Beban-Brkić, J., Volenec, V., Kolar-Begović, Z., and Kolar-Šuper, R. On Gergonne’s point of the triangle in isotropic plane. Rad HAZU, Matematičke znanosti 17, 515 (2013), 95–106.
Kolar-Šuper, R., Kolar-Begović, Z., and Volenec, V. Dual Feuerbach theorem in an isotropic plane. Sarajevo J. Math. 6, 18 (2010), 109–115.
Kolar-Šuper, R., Kolar-Begović, Z., Volenec, V., and Beban-Brkić, J. Metrical relationships in a standard triangle in an isotropic plane. Math. Commun. 10 (2005), 149–157.
Leemans, J. Propriétés du triangle déduites de la considération de formes projectives du premier et du second degré. Mathesis 51 (1937), 58–64.
Lemoine, E. Divers résultats concernant la géométrie du triangle. Assoc. Franc. Avanc. Sci. 20, 2 (1891), 130–159.
Lepiney, P. Sur le point de Feuerbach. Mathesis 36 (1922), 271–314, 271–274, 313–314.
Sachs, H. Ebene isotrope Geometrie. Vieweg–Verlag, Braunschweig/Wiesbaden, 1987.
Strubecker, K. Geometrie in einer isotropen Ebene I–III. Math. Naturw. Unterr. 15 (1962), 297–394, 297–306, 343–351, 385–394.
Thébault, V. Sur le point de Feuerbach. Nouv. Ann. Math. 14, 4 (1914), 106–119.
Thébault, V. Sur les points de Feuerbach. Math. Gaz. 20 (1936), 145–148.
Volenac, V., Kolar-Begović, Z., and Kolar-Šuper, R. Steiner’s ellipses of the triangle in an isotropic plane. Math. Pannon. 21, 2 (2010), 229–238.
Volenec, V., Kolar-Begović, Z., and Kolar-Šuper, R. Reciprocity in an isotropic plane. Rad HAZU, Matematičke znanosti 18, 519 (2014), 171–181.