Znanstvenostručni
časopis Hrvatskog društva za geometriju i grafiku Scientific and Professional Journal 
Boris Odehnal (boris.odehnal@uniak.ac.at)
Two Convergent Triangle TunnelsA semiorthogonal path is a polygon inscribed into a given
polygon such that the ith side of the path is orthogonal
to the ith side of the given polygon. Especially in the
case of triangles, the closed semiorthogonal paths are triangles which turn out to be similar to the given triangle.
The iteration of the construction of semiorthogonal paths
in triangles yields infinite sequences of nested and similar
triangles. We show that these two different sequences converge towards the bicentric pair of the triangle's Brocard
points. Furthermore, the relation to discrete logarithmic
spirals allows us to give a very simple, elementary, and new
constructions of the sequences' limits, the Brocard points.
We also add some remarks on semiorthogonal paths in
nonEuclidean geometries and in ngons. 
 Zdenka KolarBegović, Ružica KolarŠuper, Vladimir Volenec (zkolar@mathos.hr, rkolar@foozos.hr, volenec@math.hr)
Jeřabek Hyperbola of a Triangle in an Isotropic PlaneIn this paper, we examine the Jeřabek hyperbola of an
allowable triangle in an isotropic plane. We investigate different ways of generating this special hyperbola and derive its equation in the case of a standard triangle in an
isotropic plane. We prove that some remarkable points
of a triangle in an isotropic plane lie on that hyperbola
whose centre is at the Feuerbach point of a triangle. We
also explore other interesting properties of this hyperbola
and its connection with some other significant elements of
a triangle in an isotropic plane. 
Ema Jurkin (ema.jurkin@rgn.hr)
Curves of Brocard Points in Triangle Pencils in Isotropic PlaneIn this paper we consider a triangle pencil in an isotropic plane consisting of the triangles that have the same circumscribed circle. We study the locus of their Brocard points, two curves of order 4.

Si Chun Choi, N.J. Wildberger (si.choi@det.nsw.edu.au, n.wildberger@unsw.edu.au)
The Universal ParabolaWe develop classical properties, as well as some novel
facts, for the parabola using the more general framework
of rational trigonometry. This extends the study of this
conic to general fields. 
 Gunter Weiss (weissgunter@gmx.at)
The Three Reflections Theorem RevisitedIt is wellknown that, in a Euclidean plane, the product of three reflections is again a reflection, iff their axes pass through a common point. For this "Three reflections Theorem" (3RT) also nonEuclidean versions exist, see e.g. [4]. This article presents affine versions of it, considering a triplet of skew reflections with axes through a common point. It turns out that the essence of all those cases of 3RT is that the three pairs (axis, reflection direction) of the given (skew) reflections can be observed as an involutoric projectivity. For the Euclidean case and its nonEuclidean counterparts this property is automatically fulfilled. From the projective geometry point of view a (skew) reflection is nothing but a harmonic homology. In the affine situation a reflection is an indirect involutoric transformation, while "direct" or "indirect" makes no sense in projective planes. A harmonic homology allows an interpretation both, as an axial reflection and as a point reflection. Nevertheless, one might study products of three harmonic homologies, which result in a harmonic homology again. Some special mutual positions of axes and centers of the given homologies lead to elations or even to the identity, too. A consequence of the presented results are further generalisations of the 3RT, e.g. in planes with Minkowski metric, affine or projective 3space, or in circle geometries. 