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master's thesis
Četverokuti u hiperboličkoj ravnini
Zagreb: University of Zagreb, Faculty of Science, 2022. urn:nbn:hr:217:820179
Kuterovac, Doris
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Kuterovac, D. (2022). Četverokuti u hiperboličkoj ravnini (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:820179

Kuterovac, Doris. "Četverokuti u hiperboličkoj ravnini." Master's thesis, University of Zagreb, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:217:820179

Kuterovac, Doris. "Četverokuti u hiperboličkoj ravnini." Master's thesis, University of Zagreb, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:217:820179

Kuterovac, D. (2022). 'Četverokuti u hiperboličkoj ravnini', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:820179

Kuterovac D. Četverokuti u hiperboličkoj ravnini [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2022 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:820179

D. Kuterovac, "Četverokuti u hiperboličkoj ravnini", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2022. Available at: https://urn.nsk.hr/urn:nbn:hr:217:820179

Metadata
TitleČetverokuti u hiperboličkoj ravnini
Title (english)Quadrilaterals in the hyperbolic plane
AuthorDoris Kuterovac
MentorVedran Krčadinac (mentor)
Committee memberVedran Krčadinac (predsjednik povjerenstva)
Committee memberSanja Varošanec (član povjerenstva)
Committee memberMea Bombardelli (član povjerenstva)
Committee memberRobert Manger (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2022-07-20, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom diplomskom radu prisjetili smo se osnovnih činjenica o dvije vrste četverokuta u euklidskoj ravnini, pravokutnicima i paralelogramima, te obradili njihove analogone u hiperboličkoj ravnini. U drugom poglavlju nabrojali smo sedam aksioma ravninske geometrije pomoću kojih smo dokazivali teoreme u diplomskom radu. U trećem poglavlju definirali smo poligon i prikazali osnovne rezultate o poligonima. U četvrtom poglavlju diplomskog rada bavimo se pravokutnicima u euklidskoj ravnini te analogonima u hiperboličkoj ravnini: Saccherijevim četverokutima, Lambertovim četverokutima i pseudopravokutnicima. U zadnjem poglavlju ovog diplomskog rada bavimo se paralelogramima u euklidskoj ravnini, definiramo paralelne i ultraparalelne pravce u hiperboličkoj ravnini te uz pomoć njih dokazujemo egzistenciju paralelograma u hiperboličkoj geometriji.
Abstract (english)
In this thesis, we have recalled basic facts about two types of quadrilaterals in the Euclidean plane, rectangles and parallelograms, and we studied their analogues in the hyperbolic plane. In the second chapter, we listed seven axioms of plane geometry used to prove theorems in this thesis. In the third chapter, we defined polygons and showed basic results about them. In the fourth chapter, we study rectangles in the Euclidean plane and their analogues in the hyperbolic plane: Saccheri quadrilaterals, Lambert quadrilaterals, and pseudo-rectangles. In the last chapter, we defined parallelograms in the Euclidean plane and parallel and ultraparallel lines in the hyperbolic plane. We proved that parallelograms exist in the hyperbolic plane.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:820179
Study programmeTitle: Mathematics Education; specializations in: Mathematics Education
Course: Mathematics Education
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2022-09-14 08:45:30