MU03250 Projective Geometry I

Mathematical Institute in Opava
Winter 2024

The course is not taught in Winter 2024

Extent and Intensity
2/0/0. 4 credit(s). Type of Completion: z (credit).
Guaranteed by
Mathematical Institute in Opava
Prerequisites (in Czech)
TYP_STUDIA(N)
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives (in Czech)
Hlavním cílem tohoto předmětu je seznámit studenty s teoretickými základy syntetické i analytické projektivní geometrie. Předmět dále prezentuje unifikaci geometrie na základě studia působení grup a ukazuje studentům jednotící funkci matematiky na příkladu užití metod projektivní geometrie v dalších disciplínách.
Syllabus
  • 1. Projective plane. Projective extension of the Euclidean plane. Double ratio. Papp theorem. Duality principle.
    2. Projectivity of one-parameter figures. Involution.
    3. Projective definition of conic section; projective generation of conics. Pascal and Brianchon theorems.
    4. Pole and polar, applications to constructions.
    5. Pencils and rows of conics.
    6. Focus properties of conics.
    7. Contructing conics from given elements.
    8. Central collineation. Collineation of a circle and a conic.
Literature
    required literature
  • Coxeter, H.S.M. Projective geometry. Springer, 2003. ISBN 978-0-387-40623-7. info
  • K. Havlíček. Úvod do projektivní geometrie kuželoseček. Praha, 1956. info
    recommended literature
  • J. Bureš, J. Burešová. Projektivní geometrie I. Praha. info
  • Dembowski, P. Finite Geometries. Springer, 1991. ISBN 978-3540617860. info
  • Kadeřábek, Klíma, Kounovský. Desriptivní geometrie L. Praha, 1954. info
    not specified
  • Marie Chodorová. Projektivní geometrie. Oomouc, 2014. info
  • Bennett, M. K. Affine and projective geometry. New York : Wiley, 1995. ISBN 0-471-11315-8. info
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
The course is also listed under the following terms Winter 1999, Winter 2000, Winter 2001, Winter 2002, Winter 2003, Winter 2004, Winter 2005, Winter 2006, Winter 2007, Winter 2008, Winter 2009, Winter 2010, Winter 2011, Winter 2012, Winter 2013, Winter 2014, Winter 2015, Winter 2016, Winter 2017, Winter 2018, Winter 2019, Winter 2023.
  • Enrolment Statistics (Winter 2024, recent)
  • Permalink: https://is.slu.cz/course/sumu/winter2024/MU03250