Znanstvenostručni
časopis Hrvatskog društva za geometriju i grafiku Scientific and Professional Journal 
 Si Chun Choi, N. J. Wildberger(si.choi@det.nsw.edu.au, n.wildberger@unsw.edu.au)Parabolic Triangles, Poles and Centroid RelationsWe investigate affine properties of centroids formed by
three points on a parabola together with the polar triangle
formed from the tangents. And we make a wide ranging
conjecture about the extension of these results to general
conics.

 Ronaldo Garcia, Dan Reznik, Hellmuth Stachel, Mark Helman (ragarcia@ufg.brm, dreznik@gmail.com,
stachel@dmg.tuwien.ac.at,
markhelman@hotmail.com)
Steiner’s Hat: a ConstantArea Deltoid Associated with the EllipseThe Negative Pedal Curve (NPC) of the Ellipse with respect to a boundary point M is a 3cusp closedcurve which
is the affine image of the Steiner Deltoid. Over all M the
family has invariant area and displays an array of interesting
properties. 
 Boris Odehnal (boris.odehnal@uniak.ac.at)
Distance Product CubicsThe locus of points that determine a constant product of their distances to the sides of a triangle is a cubic curve in the projectively closed Euclidean triangle plane. In this paper, algebraic and geometric properties of these distance product cubics shall be studied. These cubics span a pencil of cubics that contains only one rational and nondegenerate cubic curve which is known as the Bataille acnodal cubic determined by the product of the actual trilinear coordinates of the centroid of the base triangle. Each triangle center defines a distance product cubic. It turns out that only a small number of triangle centers share their distance product cubic with other centers. All distance product cubics share the real points of inflection which lie on the line at infinity. The cubics' dual curves, their Hessians, and especially those distance product cubics that are defined by particular triangle centers shall be studied. Key words: triangle cubic, elliptic cubic, rational cubic,
trilinear distance, constant product, Steiner inellipse, triangle centers 
 Željka Milin Šipuš, Ivana Protrka, Ljiljana Primorac Gajčić (zeljka.milinsipus@math.hr, ivana.protrka@rgn.hr, lprimora@mathos.hr)
Generalized Helices on a Lightlike Cone in 3Dimensional LorentzMinkowski SpaceIn this paper we provide characterizations and give some
properties of generalized helices in 3dimensional LorentzMinkowski space that lie on a lightlike cone. Furthermore, by analyzing their projections, which turn out to
be Euclidean or Lorentzian logarithmic spiral, we present
their parametrizations. In particular, we also analyze planar generalized helices, that is planar intersections of a
lightlike cone. 
 William Beare, N. J. Wildberger (w.beare@student.unsw.edu.au, n.wildberger@unsw.edu.au)
The Feuerbach Theorem and Cyclography in Universal GeometryWe have another look at the Feuerbach theorem with a view to extending it in an oriented way to finite fields using the purely algebraic approach of rational trigonometry and universal geometry. Our approach starts with the tangent lines to three rational points on the unit circle, and all subsequent formulas involve the three parameters that define them. Tangency of incircles is treated in the oriented setting via a simplified form of cyclography. Some interesting features of the finite field case are discussed. Key words:
Feuerbach theorem, incircles, universal geometry, cyclography, finite fields 