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- Book
*3*

- Paper in journal
*10*

- Paper in proceedings
*1*

- Summary in proceedings
*8*

- M.A.
*1*

- Manuscript
*3*

- Other
*1*

**Type of paper**:*Book*

**Title:**Round Forms in the Construction

**Authors:**- Kučinić, Branko (24350)
- Kristoforović, Olga
- Saler, Ivan

**Editors**- Simović, Veselin

**Publisher**: Građevinar, časopis Saveya građevinskih inenjera i tehničara Hrvatske, Berislavićeva 6

**ISBN**: 86-81859-01-3

**Year**: 1992

**Number of pages**: 208

**Number of references**: 26

**Language**: hrvatski

**Summary**: First, there is an illustration of the basic elements and relations of the real projective space - with the method of synthetic geometry. A special attention has been given to the derivation of plane curves and surfaces. Apart from the classical derivations of the surfaces: inversion, Steiner's and Sturm's way of derivation, strophoidal, pedal in cissoide surfaces, there are two new derivations worked out in details: pedal surfaces of the congruence (1,2), and the surfaces obtained by the cubic inversion. Rulled surfaces are also being worked on, as well as the constructions connected with them. The book is illustrated by a great number of plans for designs of the objects belonging tothe higher social standard, the elements or the unities of which are general or rulled surfaces. Thus we have suggestions for schools, gymnasiums, churches, grain elevators, traffic and other objects.

**Keywords**: real projective space, structure, general surfaces, rulled surfaces, designs, gymnasiums, churches, warehouses

**Type of paper**:*Book*

**Title:**Constructive Geometry

**Authors:**- Babić, Ivanka (70564)
- Gorjanc, Sonja (176314)
- Sliepčević, Ana (43680)
- Szirovicza, Vlasta (45794)

**Editors**- Babić, Ivanka (70564)

**Publisher**: Institut građevinarstva Hrvatske

**ISBN**: 953-6085-03-8

**Year**: 1994

**Number of pages**: 268

**Number of references**: 13

**Language**: hrvatski

**Summary**: Carefully chosen tasks from descriptive geometry and its applications in tehnics are the base of this textbook. It is assigned to the students on all of the branches of tehnical university in Croatia. Introductional parts of some of the chapters supplement the existing textbook and enable better understanding of the theory and application specially in civil engineering. The book contains a lot of original tasks presented in a way which has spatial sollution, constructive sollution along with graphical presentation. That is why it gives oppotunity for selfeducation in this field.

**Keywords**: descriptive geometry, projection, Monge's method, axonometry, quoted projection, constructive elaboration of the ruled surfaces

**Type of paper**:*Book*

**Title:**Descriptive Geometry, Part I

**Authors:**- Sliepčević, Ana (43680)
- Szirovicza, Vlasta (45794)

**Publisher**: Element - HDKGKG

**ISBN**: 953-6098-93-8

**Year**: 1995

**Number of pages**: 150

**Number of references**: 10

**Language**: hrvatski

**Summary**: This book is the result of pedagogical work which authors have been doing for many years. Understanding of the rules among elements and geometrical products in the three-dimensional space has been gradualy introduced. However, it is suitable for high schools and presents a base for the successful study of the descriptive geometry on all of the branches of the tehnical university. The brief theory is followed by the solved examples with detailed explanations. The book contains 113 pictures, 40 solved tasks and 36 tasks for checking the knowledge.

**Keywords**: descriptive geometry, projection, Monge's method

**Type of paper**:*Paper in journal*

**Title:**Fast Industrial Construction of Sacral and Other Large Structures

**Authors:**- Kučinić, Branko (24350)

**Journal**: Građevinar

**Number**: 3

**ISSN**: 0350-2465

**Volume**: 45

**Year**: 1993

**Pages**: from 141 to 145

**Number of references**: 1

**Language**: hrvatski

**Summary**: The paper shows how fast construction of different structures maybe achieved with a composition of simple planar forms such as hyperbolic paraboloids or conoids, without massive construction and applying alternative materials (metal, wood, membranes). The possibilities of industrial construction of sacral structures, aswell as others covering very large areas (halls, warehousesetc.), are presented. Also shown are several types of solutions where the described forms are applied.

**Keywords**: planar form, hyperbolic paraboloid, conoid, industrial construction, sacral structure, halls, warehouses

**Type of paper**:*Paper in journal*

**Title:**A Feature of the Special Hyperbola of Isotropic Plane

**Authors:**- čurić, Vlasta (46205)

**Journal**: Sonderdruck aus Sitzungsberichte d. Oesterreichische Akademie d. Wissenschaften

**Number**: 201

**Year**: 1992

**Pages**: from 111 to 115

**Number of references**: 8

**Language**: njemački

**Summary**: A real affine plane A2 is called an isotropic plane I2, if in A2 a metric is induced by an absolute (f,F), where f is a line at infinity of A2 and F a point on f. The conic section k in I2, conveying the point F as a single point is called a special hyperbola. This paper proves that the special hyperbola, i.e. the hyperbola with one isotropic assimptote, is isotropicall analogous to the equilateral hyperbola of Euclidean plane E2.

**Keywords**: isotropic plane, affine plane, Euclidean plane, conic section, special hyperbola, equilateral hyperbola

**Type of paper**:*Paper in journal*

**Title:**Further Researches in the Fammily (MF2), II Part, Complex (VN)

**Authors:**- čurić, Vlasta (46205)

**Journal**: Rad HAZU

**ISSN**: 0351-8639

**Volume**: 456

**Year**: 1991

**Pages**: from 39 to 57

**Number of references**: 21

**Language**: njemački

**Summary**: The quadrics bundle (F2 are classified into one-parameter family(MF2) of pencils (F2), so that the mutual surface of thesepencils is a cone M2 (subset of (F2 ) with a vertex in the pointM which is element of k6. The 6. order curve k6 is made of thevertices of all bundle cones. For each of infinitely many pencilsof the group (MF2) for ray complexes are determined. The paperinvestigates the structure constituated by the rays of Niče's oriented complex and their points Z, i.e. I, when the points I, i.e. points Z of those rays are on same straight lines. Such rays determine the congruences, and the points Z, i.e. the points I associated to those rays, determine the surfaces of interesting features.

**Keywords**: quadrics, quadrics pencil and bundle, ray complex, ray congruence, surfaces, curves

**Type of paper**:*Paper in journal*

**Title:**Contribution to the Theory of the Second Order Surfaces in the Flag Space

**Authors:**- Sachs, Hans
- čurić, Vlasta (46205)

**Journal**: Rad HAZU

**ISSN**: 0351-8639

**Volume**: 456

**Year**: 1991

**Pages**: from 197 to 216

**Number of references**: 13

**Language**: njemački

**Summary**: According to H. Brauner a flag space I3(2) is a tree-dimensional affine space with an absolute (o,f,F), where f is a line in the plane of infinity o and F a point on f. In this paper the surfaces of second order in the space I3(2) are completely classified with regard to the group of isotropic motions in I3(2). All surfaces are described by normal forms and the remaining invariants are interpreted in a geometrical way. Finally some applications are given.

**Keywords**: isotropic plane, isotropic space, flag space, surfaces of second order, classify, normal-form

**Type of paper**:*Paper in journal*

**Title:**Classification Theory of Conic Section Pencil, Type IV, of the Isotropic Plane, I

**Authors:**- čurić, Vlasta (46205)
- Sachs, Hans

**Journal**: Rad HAZU

**Number**: 12

**ISSN**: 0351-8639

**Volume**: 470

**Year**: 1995

**Pages**: from 119 to 137

**Number of references**: 12

**Language**: njemački

**Summary**: 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 linear infinity f of A2 an a point F on f. In this paper we classified a conic section pencil of type IV, which is determined by one double and two real and different fundamental points. This first part describes two subtypes IV1 and IV2 with the total of 20 kinds and cases. For each of those pencils is defined its normal form. The additional classification is carried out by means of the curve of midpoints and of the curve of isotropic focal points.

**Keywords**: affine plane, isotropic plane, classify, conic section pencil, normal form

**Type of paper**:*Paper in journal*

**Title:**Isogonal Transformation and the Focal Curve of a Range of Conics

**Authors:**- Sliepčević, Ana (43680)

**Journal**: Rad HAZU

**Number**: 12

**ISSN**: 0351-8639

**Volume**: 470

**Year**: 1995

**Pages**: from 157 to 167

**Number of references**: 6

**Language**: njemački

**Summary**: In this paper the focal curve of a range of conics is connected with the pole curve of four positions of a stretchable four-barlinkage by isogonal transformation. We prove the existance of an isogonal transformation which maps the focal curve into itself and give a suitable construction of the pole curve by means of the isogonal map.

**Keywords**: focal curve, range of conics, stretchable four-bar, isogonal transformation

**Type of paper**:*Paper in journal*

**Title:**The Pencil of Conics with Two Conjugate-Imaginary Coincident Fundamental Points in the Isotropic Plane

**Authors:**- Szirovicza, Vlasta (45794)

**Journal**: Rad HAZU

**Number**: 12

**ISSN**: 0351-8639

**Volume**: 470

**Year**: 1995

**Pages**: from 13 to 35

**Number of references**: 11

**Language**: njemački

**Summary**: An 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 of A2 and the point F on f. According to K. Strubecker on I2 exists a 3-parameter group B3 of isotropic motions. In this paper we give a complete classification of pencils of conics with two conjugate-imaginary coincident fundamental points. It is shown that 3 main types and 6 subtypes of these pencils exist. We construct normal form with respect to the group B3 and give an interpretation of all geometrical invariants. Finally we give a generation of all types of pencils in a geometric way.

**Keywords**: geometry, isotropic plane, pencil of conics

**Type of paper**:*Paper in journal*

**Title:**Quartic Inversion in Space and Some of its Products

**Authors:**- Gorjanc, Sonja (176314)

**Journal**: Rad HAZU

**Number**: 12

**ISSN**: 0351-8639

**Volume**: 470

**Year**: 1995

**Pages**: from 187 to 199

**Number of references**: 11

**Language**: engleski

**Summary**: We define in this paper the transformation of the projective space, which is done in such a way that attached points are conjugated with respect to some quadric and incidental with the rays of some (1,2) congruence. It has been proved that a straight line and a plane are transformed into the space curve of order 4and quartic with a double line, respectively. We deduce some properties of these curves and surfaces and we show the connection of quartic inversion with pedal surfaces of (1,2) congruences.

**Keywords**: inversion, quartic inversion, pedal surface of (1,2) congruence, space curve of order 4 and sort II, qurtic surface with a double line

**Type of paper**:*Paper in journal*

**Title:**M-Model of the Hyperbolic H3-Space on Moebius Plane

**Authors:**- Babić, Ivanka (70564)

**Journal**: Rad HAZU

**ISSN**: 0351-8639

**Volume**: 467

**Year**: 1994

**Pages**: from 67 to 75

**Number of references**: 7

**Language**: njemački

**Summary**: In this paper the model of H3-space is obtained by means oforthogonal projection of H3-space onto the horysphere, then by isomorphic mapping of horysphere onto the Moebius plane, Hesse's relation for angle measure and Laguerre's formula for length measure is achieved in it. The model is suitable for the constructive processing of H-geometry with Euclidean means, especially after introducing the axial symetry.

**Keywords**: hyperbolic space, horysphere, Moebius-plane, model

**Type of paper**:*Paper in journal*

**Title:**Descriptive Geometry in the Hyperbolic H3-Space. Part I. Fundamental Notions. Definitions. Position Relations.

**Authors:**- Babić, Ivanka (70564)

**Journal**: Rad HAZU

**ISSN**: 0351-8639

**Volume**: 470

**Year**: 1995

**Pages**: from 167 to 186

**Language**: njemački

**Summary**: In this paper the fundamental concepts of Mongean method of projecting in H3-space, as well as positional relations are interpreted. It has been proved that some concepts, relations and elements of the Euclidean space have two or more counterparts inthe H3-space, and also, that there are elements, relations, concepts and operations in H3-space that have no counter parts in Euclidean space.

**Keywords**: M-model, H3-space, orthogonal projection, polarity

**Type of paper**:*Paper in proceedings*

**Title:**Curve of All Isotropic Focal Points

**Authors:**- Lapaine, Miljenko (80442)
- čurić, Vlasta (46205)

**Proceedings title**: Proceedings, Vol. 2

**Language**: engleski

**Place**: Tokyo, Japan

**Year**: 1994

**Pages**: from 338 to 342

**Meeting**: 6th International Conference on Engineering Computer Graphics and Descriptive Geometry

**Held**: from 08/19/94 to 08/23/94

**Summary**: Generallz, a conic section pencil is defined with four real different fundamental points (type I). In the type IV the two fundamental points coincide. Any common tangent to all curves of pencil runs through that double point. In the type VI there are two double fundamental points. In classifying the conic section pencils the curve of 3rd degree of all isotropic focal points can be applied. The graphic representation of conic section pencils can be practically performed by using a computer and plotter. In order to represent the curve of all isotropic focal points graphically, one needs its equation in a parametric form. In the paper this parametric equations are developed.

**Keywords**: isotropic geomtry, conic section pencils classification, curve of all isotropic focal points, computer graphics

**Type of paper**:*Summary in proceedings*

**Title:**M-Model of the Hyperbolic H3-Space on Moebius Plane

**Authors:**- Babić, Ivanka (70564)

**Editors**- Sachs, Hans

**Proceedings title**: Kolokvij za konstruktivnu geometriju u spomen prof. dr. H. Braunera

**Language**: njemački

**Place**: Leoben, Austrija

**Year**: 1991

**Meeting**: Kolokvij za konstruktivnu geometriju

**Held**: from 04/28/91 to 05/03/91

**Summary**: In this paper the model of H3-space is obtained by means of orthogonal projection of H3-space onto the horysphere, then by isomorphic mapping of horysphere onto the Moebius plane, Hesse's relation for angle measure and Laguerre's formula for length measure is achieved in it. The model is suitable for the constructive processing of H-geometry with Euclidean means, especially after introducing the axial symetry.

**Keywords**: hyperbolic space, horysphere, Moebius-plane, model

**Type of paper**:*Summary in proceedings*

**Title:**Isogonal Transformation and the Focal Curve of a Range of Conics

**Authors:**- Sliepčević, Ana (43680)

**Editors**- Sachs, Hans

**Proceedings title**: Kolokvij za konstruktivnu geometriju u spomen prof. dr. H. Braunera

**Language**: njemački

**Place**: Leoben, Austrija

**Year**: 1991

**Meeting**: Kolokvij za konstruktivnu geometriju

**Held**: from 04/28/91 to 05/03/91

**Summary**: In this paper the focal curve of a range of conics is connected with the pole curve of four positions of a stretchable four-barlinkage by isogonal transformation. We prove the existance of an isogonal transformation which maps the focal curve into itself and give a suitable construction of the pole curve by means of Wthe isogonal map.

**Keywords**: focal curve, range of conics, stretchable four-bar, isogonal transformation

**Type of paper**:*Summary in proceedings*

**Title:**The Pencil of Conics with Two Conjugate-Imaginary Coincident Fundamental Points in the Isotropic Plane

**Authors:**- Szirovicza, Vlasta (45794)

**Editors**- Sachs, Hans

**Proceedings title**: Kolokvij za konstruktivnu geometriju u spomen prof. dr. H. Braunera

**Language**: njemački

**Place**: Leoben, Austrija

**Year**: 1991

**Meeting**: Kolokvij za konstruktivnu geometriju

**Held**: from 04/28/91 to 05/03/91

**Summary**: An 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 of A2 and the point F on f. According to K. Strubecker on I2 exists a 3-parameter group B3 of isotropic motions. In this paper we give a complete classification of pencils of conics with two conjugate-imaginary coincident fundamental points. It is shown that 3 main types and 6 subtypes of these pencils exist. We construct normal form with respect to the group B3 and give an interpretation of all geometrical invariants. Finally we give a generation of all types of pencils in a geometric way.

**Keywords**: geometry, isotropic plane, pencil of conics

**Type of paper**:*Summary in proceedings*

**Title:**Classification Theory of Conic Section Pencil, Type IV, of the Isotropic Plane, II

**Authors:**- čurić, Vlasta (46205)

**Editors**- Sachs, Hans

**Proceedings title**: Kolokvij za konstruktivnu geometriju u spomen prof. dr. H. Braunera

**Language**: njemački

**Place**: Leoben, Austrija

**Year**: 1991

**Meeting**: Kolokvij za konstruktivnu geometriju

**Held**: from 04/28/91 to 05/03/91

**Summary**: In this paper we continue one complete classication of pencils ofconics (Type IV) with two real and different fundamental pointsand one double fundamental point. With respect to the 3-parameter group B3 of isotropic motions we construct normal forms for the 13 remaining main-types and we study some subtypes. Finaly we give an interpretation of all geometrical invariants, using the curve of midpoints and the curve of focal points of the pencil.

**Keywords**: affine plane, isotropic plane, classify, conic section pencil, normal form

**Type of paper**:*Summary in proceedings*

**Title:**Special Hyperbola in I2 as Isotropic Analogue of Equilateral Hyperbola in E2

**Authors:**- čurić, Vlasta (46205)

**Editors**- Sachs, Hans

**Proceedings title**: 7. ungarisch-oesterreichisches Geometrie-Symposium

**Language**: njemački

**Year**: 1992

**Meeting**: 7. ungarisch-oesterreichisches Geometrie-Symposium

**Held**: from 04/26/92 to 05/02/92

**Summary**: Equilateral hyperbola of Euclidean plane has got the properties by which it is distinguished from the other conics. If these properties should be transferred into the isotropic plane, it is to be seen, that they of all properties characterize a special hyperbola of this plane. It proves that the special hyperbola is an isotropic analogue of the equilateral hyperbola in the Euclidean plane.

**Keywords**: isotropic plane, affine plane, Euclidean plane, conic section, special hyperbola, equilateral hyperbola

**Type of paper**:*Summary in proceedings*

**Title:**Classification Theory of Conic Section Pencil, Type VI, of the Isotropic Plane

**Authors:**- čurić, Vlasta (46205)

**Editors**- Sachs, Hans

**Proceedings title**: Welttagung ueber Geometrie

**Language**: njemački

**Year**: 1995

**Pages**: from 29 to 29

**Meeting**: Welttagung ueber Geometrie

**Held**: from 05/14/95 to 05/19/95

**Summary**: In an isotropic plane I2 a metric is induced by an absolute (f,F), consisting of the line at infinity f of I2 and a point F on f. In this paper a complete classification of pencils of conics with two real double fundamental points - typ VI - is given. We construct normal forms for all main types and we study 11 subtypes. Finally we give an interpretation of some geometrical invariants, using the curve of midpoints and the curve of focal points of the pencil.

**Keywords**: affine plane, isotropic plane, classify, conic section pencil, normal form

**Type of paper**:*Summary in proceedings*

**Title:**Descriptive Geometry in the Hyperbolic H3-Space, Part I

**Authors:**- Babić, Ivanka (70564)

**Editors**- Molnar, Emil

**Proceedings title**: Konstruktive Geometrie

**Language**: njemački

**Place**: Budapest, Mađarska

**Year**: 1995

**Meeting**: Konstruktive Geometrie

**Held**: from 09/11/95 to 09/15/95

**Summary**: In this paper the fundamental concepts of Mongean mathod of projecting in H3-space, as well as positional relations are interpreted. It has been proved that some concepts, relations and elements of the Euclidean space have two or more counterparts in the H3-space, and also, that there are elements, relations, concepts and operations in H3-space that have no counterparts in Euclidean space.

**Keywords**: M-model, H3-space, orthogonal projection, polarity

**Type of paper**:*Summary in proceedings*

**Title:**Quartic Inversion in Space and Some of its Products

**Authors:**- Gorjanc, Sonja (176314)

**Editors**- Molnar, Emil

**Proceedings title**: Konstruktive Geometrie

**Language**: engleski

**Place**: Budapest, Mađarska

**Year**: 95

**Meeting**: Konstruktive Geometrie

**Held**: from 09/11/95 to 09/19/95

**Summary**: Quartic inversion in projective space is defined, and some of its products are deduced.

**Keywords**: inversion, quartic inversion, pedal surface of (1,2) congruence,space curve of order 4 and sort II, qurtic surface with a doubleline

**Type of paper**:*M.A.*

**Title:**Object-Oriented Model of Projective Geometry

**Faculty**: Tehnika fakulteta - Elektrotehnika, računalnitvo in informatika Univerza v Mariboru

**Date of defense**: 06/11/93

**Language**: hrvatski

**Number of pages**: 177

**Summary**: This thesis presents the kernel of the library of new data types(in object-oriented programming called classes) that representbasic concepts of projective geometry of n-dimensional real andcomplex projective space. The classes can be divided in threegroups: primary geometric elements (points and hyperplanes),collections of points (lists and ordered sets) and projectivetransformations. The representation of primary elements and thetransformations corresponds to vector and matrix representationin algebraic treatment respectively. The functions and operatorsof the classes are based on procedures of the algebraic model.

**Keywords**: projective geometry, geometric element, projective transformation, projection, computer graphics, object-oriented programming

**Type of paper**:*Manuscript*

**Title:**Classification Theory of Conic Section Pencil, Type IV, of the Isotropic Plane, II

**Authors:**- čurić, Vlasta (46205)
- Sachs, Hans

**Language**: njemački

**Summary**: In this paper we continue one complete classication of pencils ofconics (Type IV) with two real and different fundamental pointsand one double fundamental point. With respect to the 3-parametergroup B3 of isotropic motions we construct normal forms for the13 remaining main-types and we study some subtypes. Finaly wegive an interpretation of all geometrical invariants, using thecurve of midpoints and the curve of focal points of the pencil.

**Keywords**: affine plane, isotropic plane, classify, conic section pencil, normal form

**Other**: PRIHVAĆENO ZA TISAK U RADU HAZU

**Type of paper**:*Manuscript*

**Title:**Descriptive Geometry in the Hyperbolic H3-Space. Part II. Metric Investigations

**Authors:**- Babić, Ivanka (70564)

**Language**: njemački

**Summary**: There are three fundamental metric problems referring to thedescriptive geometry of H3-space constructively worked out andproved in this paper. The real size of the plane figure is determined throughH-rotation of the plane belonging to the given figure around its trace into the plane of the picture. H-perspective collineationis established between the projection and the rotated position ofthe field of plane points. Mutual perpendicularity of straightline and plane is interpreted in the same way as in the Euclideanspace, while the solving method has the characteristic od beingadjusted to the M-model.

**Keywords**: M-model, H3-space, H-rotation of plane, H-perspective collineation, polarity

**Other**: PRIHVAĆENO ZA TISAK U RADU HAZU

**Type of paper**:*Manuscript*

**Title:**Classification Theory of Conic Section Pencil, Type VI, of the Isotropic Plane

**Authors:**- čurić, Vlasta (46205)

**Language**: njemački

**Summary**: In an isotropic plane I2 a metric is induced by an absolute (f,F), consisting of the line at infinity f of I2 and a point F on f. In this paper a complete classification of pencils of conics with two real double fundamental points - typ VI - is given. We construct normal forms for all main types and we study 11 subtypes. Finally we give an interpretation of some geometrical invariants, using the curve of midpoints and the curve of focal points of the pencil.

**Keywords**: affine plane, isotropic plane, classify, conic section pencil, normal form

**Other**: Prihvaćeno za tisak u međunarodnom časopisu MATHEMATICA PANNONICA

**Type of paper**:*Other*

**Title:**Computer Application in a Classification of Conic Section Pencils in the Isotropic Plane

**Authors:**- Lapaine, Miljenko (80442)
- čurić, Vlasta (46205)
- Sachs, Hans

**Type of work**: Poster na First European Congress of Mathematics, Paris 1992.

**Language**: engleski

**Summary**: In classifying of conic section pencils the application ofcomputer and plotter can be useful. The poster brifly describesthe mathematical basis of the own software which is developed inorder to enable the fully automated representation of conicsection pencils. The classification is based on the two specialcurves: the curve of all centres of conic sections, and the curveof all isotropic fical points, so that these curves are alsorepresented. The procedure is illustrated with some figures ofpencils where the fundamental points are a double point and twodifferent real points in the isotropic plane.

**Keywords**: isotropic geometry, classification of conic section pencils, computer application

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