Znanstveno-stručni časopis
Hrvatskog društva za geometriju i grafiku

Scientific and Professional Journal
of the Croatian Society for Geometry and Graphics

Daniel Lordick (lordick@math.tu-dresden.de)

Shade Lines of Curved Surfaces - Linear Approach to Involution of Conjugate Tangents at Points of Translation Surfaces

In KoG 6 we introduced a global approach to the tangents of the shade lines of curved surfaces. The constructions are made by using an accompanying ruled surface along the shade line. In this paper the method is expanded to translation surfaces. In that way we get a linear access to the involution of conjugate tangents in those points of a surface where the curvature at two conjugate tangents is given. At the end of the paper a helical surface with circular cross section is handled as translation surface, which leads to additional elegant constructions for the tangents of its shade line. For more details on the general subject see [4].

Keywords: curved surface, Dupin-indicatrix, ruled surface, shades and shadows

Article in PDF.

Ana Sliepčević (anasli@juraj.gradnz.grad.hr)

Pencil of circles in isotropic plane

The model of an isotropic plane with absolute figure (f,F) in finiteness is studied. In comparation with Euclidean plane, where pencil of circles can be set only on five different ways, it is shown that in an isotropic plane it can be done on nine ways. A circle is constructed for every given pencil.

Keywords: geometry, isotropic plane, isotropic circle

Article in PDF.

Jasna Kos-Modor, Ema Jurkin (ejurkin@rgn.hr)


The faults are basic structural units of lithosphere. They begin to create by the cracking and moving of the rocks because of the gravitation, expansion or compression forces. Two blocks of the rocks are formed, fault walls - hanging wall and foot wall, which are moving along the fault plane. In view of the moving of the hanging wall with respect to the foot wall, we distinguish the normal fault and the reverse fault. In the projection with heights, the normal fault and the reverse fault with two profiles are shown.

Keywords: projection with heights, fault, fault plane, fault walls

Article in PDF.

Sanja Hak, Sonja Gorjanc, Mario Uroš (sgorjanc@grad.hr)

Visualizations of Gaussian and Mean Curvatures by Using Mathematica

The paper gives an overview of the program written in the language Mathematica, which enables colouring of a surface with the colour that is the function of its Gaussian and mean curvatures, as well as drawing the graphs of those functions. Ten examples of visualizations obtained by the use of that program are presented. The article is a small extract from the students' paper which was awarded Rector's Prize in 2004.

Keywords: Gaussian curvature, mean curvature, surface, visualization

Article in PDF.

Jelena Beban Brkić, Vladimir Volenec (jbeban@geof.hr)

Butterflies in the Isotropic Plane

A real affine plane A2 is called an isotropic plane I2, if in A2 a metric is induced by an absolute {f, F}, consisting of the line at infinity f of A2 and a point F Î f. In this paper the well-known Butterfly theorem has been adapted for the isotropic plane. For the theorem that we will further-on call an Isotropic butterfly theorem, four proofs are given.

Keywords: isotropic plane, butterfly theorem

Article in PDF.