Geometrija izotropne ravnine

master's thesis

• Author: Ivona Čatipović
• Mentor: Ema Jurkin (mentor)
• Committee member: Ema Jurkin (predsjednik povjerenstva)
• Committee member: Željka Milin-Šipuš (član povjerenstva)
• Committee member: Boris Guljaš (član povjerenstva)
• Committee member: Marko Vrdoljak (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2018-07-16, 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: izotropna ravnina; euklidska ravnina; konike; trokut; kružnica
• Keywords (english): isotropic plane; Euclidean plane; conics; triangle; circle
• Language: croatian
• URN:NBN: urn:nbn:hr:217:779261
• Study programme: Title: 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 resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2018-11-22 13:57:46