#### Rad HAZU, Matematičke znanosti, Vol. 18 (2014), 171-181.

### RECIPROCITY IN AN ISOTROPIC PLANE

### Vladimir Volenec, Zdenka Kolar-Begović and Ružica Kolar-Šuper

Department of Mathematics, University of Zagreb, 10 000 Zagreb, Croatia

*e-mail:* `volenec@math.hr`
Department of Mathematics, University of Osijek, 31 000 Osijek, Croatia

*e-mail:* `zkolar@mathos.hr`

Faculty of Teacher Education, University of Osijek, 31 000 Osijek, Croatia

*e-mail:* `rkolar@ufos.hr`

**Abstract.** The concept of reciprocity with respect to a triangle is
introduced in an isotropic plane. A number of statements about the properties
of this mapping is proved. The images of some well known elements
of a triangle with respect to this mapping will be studied.

**2010 Mathematics Subject Classification.**
51N25.

**Key words and phrases.** Isotropic plane, standard triangle, reciprocity, Steiner point.

**Full text (PDF)** (free access)

**References:**

- J. Beban-Brkić, R. Kolar-Šuper, Z. Kolar-Begović and
V. Volenec,
*On Feuerbach's theorem and a pencil of circles
in the isotropic plane*,
J. Geom. Graph. **10** (2006), 125-132.

MathSciNet

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

MathSciNet

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

MathSciNet

- R. Kolar-Šuper, Z. Kolar-Begović, V. Volenec and
J. Beban-Brkić,
*Isogonality and inversion in an
isotropic plane*,
Int. J. Pure Appl. Math. **44** (2008), 339-346.

MathSciNet

- J. Leemans,
Question 2489, Mathesis
**48** (1934), 260.

- A. Vandeghen,
*Some remarks on the isogonal and cevian
transform. Alignments of remarkable points of a triangle*,
Amer. Math. Monthly **72** (1965), 1091-1094.

MathSciNet

- V. Volenec, J. Beban-Brkić, R. Kolar-Šuper and
Z. Kolar-Begović,
*Orthic axis, Lemoine line and
Longchamps' line of the triangle in **I*_{2},
Rad Hrvat. Akad. Znan. Umjet. Mat. Znan. **16** (2009), 13-19.

MathSciNet

- V. Volenec, Z. Kolar-Begović and R. Kolar-Šuper,
*Steiner's ellipses of the triangle in an isotropic plane*,
Math. Pannon.
**21** (2010), 229-238.

MathSciNet &

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