Caseyev teorem

master's thesis

• Author: Adam Naglaš
• Mentor: Mea Bombardelli (mentor)
• Committee member: Mea Bombardelli (predsjednik povjerenstva)
• Committee member: Dalibor Paar (član povjerenstva)
• Committee member: Andrej Dujella (član povjerenstva)
• Committee member: Zvonko Iljazović (član povjerenstva)
• Committee member: Mario Basletić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2019-02-28, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom diplomskom radu bavimo se Caseyevim teoremom. U prvom poglavlju iskazujemo i dokazujemo Ptolomejev teorem kako bismo pobliže razumjeli Caseyev teorem, te definiramo osnovne pojmove koje koristimo kroz rad. U drugom poglavlju pažnju posvećujemo inverziji koja se koristi u dokazivanju Caseyevog teorema. U trećem poglavlju iskazujemo i dokazujemo Caseyev teorem na nekoliko načina i dokazujemo specijalne slučajeve Caseyevog teorema. Sami kraj rada posvećen je primjeni Caseyevog teorema u dokazivanju drugih teorema i u rješavanju geometrijskih zadataka.

Abstract (english)

In this graduate thesis we are dealing with Casey’s theorem. In the first chapter, we formulate and prove Ptolemy’s theorem to better understand Casey’s theorem, and define the basic terms we use through graduate thesis. In the second chapter, we dedicate to the inversion used to prove Casey’s theorem. In the third chapter, we phrase and prove Casey’s theorem in several ways and prove the special cases of Casey’s theorem. The end of the graduate thesis is dedicated to the application of Casey’s theorem in proving other theorems and in solving geometric problems.

• Keywords: Caseyev teorem; Ptolomejev teorem; geometrijski zadaci; inverzija
• Keywords (english): Casey’s theorem; Ptolemy’s theorem; geometric problems; inversion
• Language: croatian
• URN:NBN: urn:nbn:hr:217:920742
• Study programme: Title: Mathematics and Physics Education; specializations in: Mathematics and Physics Education; Course: Mathematics and Physics Education; Study programme type: university; Study level: integrated undergraduate and graduate; Academic / professional title: magistar/magistra edukacije matematike i fizike (magistar/magistra edukacije matematike i fizike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-08-30 11:55:35