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master's thesis
Geometrija izotropne ravnine
Zagreb: University of Zagreb, Faculty of Science, 2018. urn:nbn:hr:217:779261
Čatipović, Ivona
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Čatipović, I. (2018). Geometrija izotropne ravnine (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:779261

Čatipović, Ivona. "Geometrija izotropne ravnine." Master's thesis, University of Zagreb, Faculty of Science, 2018. https://urn.nsk.hr/urn:nbn:hr:217:779261

Čatipović, Ivona. "Geometrija izotropne ravnine." Master's thesis, University of Zagreb, Faculty of Science, 2018. https://urn.nsk.hr/urn:nbn:hr:217:779261

Čatipović, I. (2018). 'Geometrija izotropne ravnine', Master's thesis, University of Zagreb, Faculty of Science, accessed 01 June 2024, https://urn.nsk.hr/urn:nbn:hr:217:779261

Čatipović I. Geometrija izotropne ravnine [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2018 [cited 2024 June 01] Available at: https://urn.nsk.hr/urn:nbn:hr:217:779261

I. Čatipović, "Geometrija izotropne ravnine", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2018. Available at: https://urn.nsk.hr/urn:nbn:hr:217:779261

Metadata
TitleGeometrija izotropne ravnine
AuthorIvona Čatipović
MentorEma Jurkin (mentor)
Committee memberEma Jurkin (predsjednik povjerenstva)
Committee memberŽeljka Milin-Šipuš (član povjerenstva)
Committee memberBoris Guljaš (član povjerenstva)
Committee memberMarko Vrdoljak (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2018-07-16, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U radu se definirala izotropna ravnina kao realna projektivna ravnina u kojoj je metrika inducirana realnim pravcem \(f\) i s njim incidentnom tockom \(F\). Nakon toga se odredila grupa sličnosti i grupa gibanja izotropne ravnine te su dani teoremi vezani za trokut u izotropnoj ravnini, a koji su analogni teoremima koje vrijede u euklidskoj ravnini. Također su dane analogije nekih pojmova u trokutu kao što su visina, simetrala kuta i težište. U trećem poglavlju se definirala krivulja 2. reda u izotropnoj ravnini te je dana njihova klasifikacija. Klasifikacija konika se napravila gledajući međusobni položaj konike i apsolutne figure. Također dani su teoremi vezani za kružnicu koji vrijede u izotropnoj ravnini, a koji su analogni teoremima u euklidskoj ravnini.
Abstract (english)
In this thesis, the isotropic plane was defined as the real projective plane in which the metric was induced by a real line \(f\) and a real point \(F\) incident with it. Subsequently, a group of similarities and a group of motions were determined. Some theorems related to a triangle in the isotropic plane were proven and they were compared with the analogues theorems in Euclidean plane. We defined analogue concepts of a triangle such as height, angle bisector and triangle centroid. In the third chapter, curve of the 2nd order in the isotropic plane were studied and their classification was given. The classification was made according to the position of the conic with respect to the absolute figure. Therefore, the intersection of the conic and the absolute line was observed. Moreover, the counterparts of some well known theorems related to a circle in the Euclidean plane were proved.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:779261
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 on2018-11-22 13:57:46