Section of Geometry

„Do not worry about your difficulties in mathematics,
I assure you that mine are greater - Albert Einstein”

Welcome to our pages

Research

Teaching and Scientific Profile

Department of Geometry is one of the oldest institutes of Faculty of Mathematics and Physics. It was established in the year 1960. It provides education of the teachers of mathematics and descriptive geometry for the secondary comprehensive and grammar schools and a training of specialists in computer geometry and computer graphics.

There are two sections at the department: the section of geometry and topology and the section of descriptive geometry and computer graphics.

The department provides a wide range of lectures, exercises and seminars on various subjects at the undergraduate level such as calculus, linear algebra, basic geometry, higher geometry and history of mathematics for all teacher training students and special courses and seminars on some parts of geometry and topology for the students of mathematics. It plays a major role in the education and supervision of postgraduates and in supplementary forms of study.

Research Topics

Scientific and research activities of the department are devoted mainly to algebraic and differential geometry and topology, applied geometry and computer graphics, history of mathematics and didactics of mathematics. In the framework of these activities the members of the department staff have supervised over 25 postgraduates to their PhD-degree and over 100 post-graduates to their academic degree RNDr.

The authors from the department have contributed essentially to the edition of four university text-books and about 10 text-books and workbooks in mathematics for schools. They are also the authors of several monographs and ecyclopaedic works.

The department is engaged in a wide cooperation with several inland and foreign university institutions (Germany: Halle, Leipzig, Potsdam etc.; Austria: Vienna, Graz; Hungary: Budapest; Italy: Bologna, Palermo), and it is a member of an institutionalized system of the international scientific and education cooperation. It has held several international summer schools.

The members of the department staff often give lectures as invited participants of international symposia and conferences (Austria, Germany, Czech Republic etc.) and they were acting as visiting professors in foreign countries several times for a longer time.

Graduates are usually appointed to the posts of teachers at secondary or grammar schools or universities, they can also be employed in various branches of industry (design), services, financial institutes etc.

Selected publications

Monographs (in Slovak):
  • V. Svitek:
    Logicke zaklady geometrie. Bratislava, SPN 1969
  • J. Cizmar, V. Zatko (spoluautori):
    Encyklopaedia of Mathematics. Bratislava, Obzor 1967 (1. vydanie), 1978 (2. vydanie), 1981 (3. vydanie)
  • J. Cizmar:
    Grupy geometrickych transformacii. Bratislava, Alfa 1984
Text-books (in Slovak):
  • V. Zatko (spoluautor):
    Geometria 1 (ucebny text pre VS). Bratislava, SPN 1985
  • M. Bozek (spoluautor):
    Geometria 2 (ucebny text pre VS). Bratislava, SPN 1987
  • V. Pijak, V. Zatko (spoluautor):
    Konstrukcna geometria (ucebnica pre VS). Bratislava, SPN 1985
  • T. Hecht, Z. Sklenarikova:
    Metody riesenia uloh (ucebnica pre VS). Bratislava, SPN 1992
  • M. Bozek (spoluautor):
    Matematika 2 (ucebnica pre gymnazia). Bratislava, SPN 1985-1990
  • J. Cizmar (hlavny autor):
    Matematika 6. I, II, SPN, Bratislava-Praha 1989-1996
  • J. Cizmar (spoluautor):
    Matematika 7. I, II, SPN, Bratislava-Praha 1990-1996
  • S. Solcan:
    Projektivna geometria (skriptum). UK Bratislava, 1994
  • M. Bozek:
    Matematika 2 (zvazok 3) (ucebnica pre gymnazia). Bratislava, Orbis Pictus, 1998
  • P. Chalmoviansky (spoluautor):
    Zlozitost geometrickych algoritmov (skriptum). UK Bratislava, 2001
  • Z. Sklenarikova, J. Cizmar:
    Elementarna geometria euklidovskej roviny (skriptum). Univerzita Komenskeho, Bratislava 2002
Selected from earlier publication:
  • E. Boda, W.Vogel:
    On system of parameters, local intersection multiplicity abd Bezout´s theorem. Proceedings of the American Mathematical Society, Vol. 78, (1980), p. 1-7
  • E. Boda:
    Einige Eigenschaften der Parameterideale und ihre Anwendung für Buchsbaum Ringe. Math.Slovaca 29, 1979, No. 3, 239-244
  • E. Boda:
    A note on the intersection multiplicity. Math. Slovaca 32 1982, No. 2, 177-181.
  • M. Bozek, K. Drechsler:
    Morphismen von Fahnenmengen. Acta Mathematica Universitatis Comenianae, Vol. 58-59, (1991), p. 135-148
  • M. Bozek, K. Drechsler:
    Singularities on Flag Spaces. Math. Slovaca 49, 1999, 503-514
  • M. Bozek:
    Existence of generalized affine symmetric spaces of arbitrary order. Colloquium Math. 47 (1982), 283-293.
  • J. Cizmar:
    Eine kubische Transformation in Sn, Acta Mathematica Universitatis Comenianae, Roc. 19, (1968), s. 75-98
  • J. Cizmar:
    Eine Involution des 5. Grades. Acta Mathematica Universitatis Comenianae, Roc. 20 (1969), s. 91-100
  • J. Cizmar:
    Algebricke krivky I. Matematicke obzory, Roc. 14 (1979), s. 5-22
  • J. Cizmar:
    Algebricke krivky II. Matematicke obzory, Roc. 15 (1980), s. 11-20
  • P. Chalmoviansky:
    Simple shaping of 3d body: Spring Conference on Computer Graphics SccG 1997, UK Bratislava
  • P. Chalmoviansky:
    Interpolation of Curve Net. SCCG'96 Proceedings, UK Bratislava, 1996
  • S. Kudlickova:
    Shape modification of "rational" B-spline curves: Proceedings of the 8th Spring School on Computer Graphics and its Applications, UK Bratislava, 1992
  • S. Kudlickova:
    Composite Surfaces from (2,2) Rational Patches. SCG'99 Proceedings, Vol. 8, STU Bratislava 1999
  • Z. Sklenarikova:
    Antihomographies. The representation of antiinvolutions in the three-dimensional euclidean space. Acta Facultatis Rerum Naturalium Universitatis Comenianae: Mathematica, Vol. 32, (1975), s. 13-29
  • S. Solcan:
    Über die Abhangigkeit der Buchsbaum Eigenschaft von der Charakteristik des Grundkörpers. Math. Slovaca 31, 1981, No. 4, 437-444.
  • S. Solcan:
    Über eine Eigenschaft des Multiplizitatssymbol. Beitrage zur Algebra und Geometrie 19(1985), 59-63.
  • P. Schenzel, S. Solcan:
    On ideals generated by square-free monomials in regular sequences. Math. Nachr. 141(1989), 335-341.
  • V. Zatko:
    O kuzeloseckach urcenych vseobecnymi rovnicami. Matematicke obzory 23 (1984), 27-36.
  • V. Zatko:
    On matrix expresions of beta-splines: 8th Spring School on Computer Graphics and its Applications, Bratislava 25.-28. 5. 1992
  • V. Zatko:
    On multisided Bezier patches. Proceedings of 5th International Conference Computer Graphics '93, Budmerice 1993
Recent Papers:
  • S. Kudlickova:
    Pravouhla axonometria a numericke vycislenia. Proceedings of Seminars on Computational Geometry, Vol. 9, Bratislava STU, 2000
  • P. Chalmoviansky:
    Subdivision surfaces in geometric modeling. Proceedings of Seminars on Computational Geometry, Vol. 9, Bratislava: STU, 2000
  • S. Solcan:
    On Computation of Symbolic Primes of some Monomial Curves in A4. Acta Mathematica Universitatis Comenianae LXIX, 1, (2000)
  • V. Zatko:
    Some new books on CAGD from viewpoint of the geometers or to quote or not to quote? Proceedings of Seminars on Computational Geometry, Vol. 9, Bratislava: STU, 2000
  • J. Cizmar:
    Tradicne vyucovanie a modernizacne trendy v matematike. In: Zbornik prednasok z medzinarodnej konferencie Nove trendy vo vyucbe matematiky, Katedra matematiky Fakulty ekonomiky a manazmentu Slovenskej polnohospodarskej univerzity v Nitre, Nitra 23. 5. 2001, str. 6-10
  • J. Cizmar:
    Zaciatky modernej algebry na Slovensku. In: Matematika v promenach veku II. Dejiny matematiky, svazek 16. Prometheus, Praha 2001, str. 251-262. ISBN 80-7196-218-X
  • J. Cizmar:
    Mascheroniho a Steinerove konstrukcie. In: Proceedings of Symposium on Computational Geometry SCG´2001, Volume 10, STU Bratislava, 2001, str. 23-36
  • M. Bozek:
    Comparison of two concepts for non-overlapping plane figures, Proceedings of Seminars on Computational Geometry, Vol. 10, Bratislava: STU, 2001
  • P. Chalmoviansky:
    Subdivision Surfaces in Geometric Modelling. ERCIM News No. 44, January 2001
  • S. Solcan:
    On Computation of Symbolic Primes of some Monomial Curves in A4. AMUC LXIX, 1, (2000)
  • S. Kudlickova:
    Racionalne plochy tenzoroveho sucinu. Sbornik z 21. Konference o geometrii a pocitacove grafice, Brno, Jednota ceskych matematiku a fyziku, 2001
  • S. Kudlickova:
    Some remarks on C-B spline curves. Proceedings of Seminars on Computational Geometry, Vol. 10, Bratislava: STU, 2001
  • Z. Sklenarikova:
    Z dejin deskriptivnej geometrie v Rakusko-Uhorsku. In: Matematika v promenach veku II. Dejiny matematiky, svazek 16. Prometheus, Praha 2001
  • Z. Sklenarikova:
    Emil Müller a modernizacne tendencie vo vyucovani deskriptivnej geometrie na zaciatku 20.storocia. In: Zbornik prednasok z medzinarodnej konferencie „Nove trendy vo vyucbe matematiky“. SPU Nitra 2001
  • S. Kudlickova:
    The composite rational curves and their smoothness. Periodica Polytechnica, Seria Mech. Eng., Vol. 46, No. 1, (2002)
  • S. Kudlickova:
    Patch with NURBS boundary curves. Proceedings of Seminars on Computational Geometry, Vol. 11, Bratislava: STU, 2002
  • M. Bozek:
    On periodical placements of polygons. Proceedings of Seminars on Computational Geometry, Vol. 11, Bratislava: STU, 2002
  • E. Boda:
    O spolocnych bodoch rovinnych algebraickych kriviek. In: Matematika vo vyucbe, vyskume a praxi 2002, Nitra, 2002
  • J. Cizmar:
    Metricke roviny a grupy transformacii. In: Proceedings of Symposium on Computational Geometry SCG´2002, Volume 11, STU Bratislava, 2002, str. 17-20. ISBN 80-227-1773-8
  • J.Cizmar:
    Ucitel matematiky - nezastupitelny faktor modernizacie jej vyucovania. In: Zbornik vedeckych prac z medzinarodnej vedeckej konferencie „Matematika vo vyucbe, vyskume a praxi 2002“, Nitra 2002, str. 33-38
  • Z. Sklenarikova:
    O Gergonnovom rieseni Apolloniovej ulohy. In: Zbornik vedeckych prac z medzinarodnej vedeckej konferencie „Matematika vo vyucbe, vyskume a praxi 2002“. SPU Nitra 2002
  • S. Solcan:
    Monomialne krivky C(p2, p2+p, p2+p+1,(p+1)2) ako mnozinove uplne prieniky. In: Matematika vo vyucbe, vyskume a praxi 2002. SPU Nitra, 2002
  • S. Kudlickova:
    The Composite Rational Curves and their Smoothness, Periodica polytechnica, Mechanical Engineering 2002 46/1, Budapest University of Technology and Economics, Hungary
  • S.Kudlickova:
    Patch with NURBS Boundary Curves, Proceedings of Symposium on Computational Geometry, SCG’ 2002
  • V. Zatko:
    Paraboloids in geometric modelling. Proceedings of Seminars on Computational Geometry, Vol. 11, Bratislava: STU, 2002
  • E. Boda:
    O pocte rieseni systemu algebraickych rovnic. In.: „Matematika vo vyucbe, vyskume a praxi 2003“. SPU Nitra, 2003
  • Z. Sklenarikova:
    O Soddiho retazci gulovych ploch. In.: „Matematika vo vyucbe, vyskume a praxi 2003“. SPU Nitra, 2003
  • S. Solcan:
    O troch involuciach. In.: „Matematika vo vyucbe, vyskume a praxi 2003“. SPU Nitra, 2003
  • M. Bozek:
    On Periodical Placements with Symmetries. In: Proceedings of Syposium on Computational Geometry SCG 2003 (Vol. 12). ISBN 80-227-1914-5. Slovak University of Technology, Bratislava 2003, 9-13.