Četverokuti u hiperboličkoj ravnini

master's thesis

• Title (english): Quadrilaterals in the hyperbolic plane
• Author: Doris Kuterovac
• Mentor: Vedran Krčadinac (mentor)
• Committee member: Vedran Krčadinac (predsjednik povjerenstva)
• Committee member: Sanja Varošanec (član povjerenstva)
• Committee member: Mea Bombardelli (član povjerenstva)
• Committee member: Robert Manger (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2022-07-20, 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: pravokutnik; paralelogram; poligon; euklidska ravnina; hiperbolička ravnina; Saccherijevi četverokuti; Lambertovi četverokuti; pseudopravokutnici
• Keywords (english): rectangle; parallelogram; polygon; Euclidean plane; hyperbolic plane; Saccheri quadrilaterals; Lambert quadrilaterals; pseudorectangles
• Language: croatian
• URN:NBN: urn:nbn:hr:217:820179
• 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: 2022-09-14 08:45:30