Miquelov teorem

master's thesis

• Title (english): Miquel's theorem
• Author: Tena Novosel
• Mentor: Marija Galić (mentor)
• Committee member: Marija Galić (predsjednik povjerenstva)
• Committee member: Aleksandra Čižmešija (član povjerenstva)
• Committee member: Dražen Adamović (član povjerenstva)
• Committee member: Matko Ljulj (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2024-02-28, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom diplomskom radu proučavamo Miquelov teorem i njegove varijante. Rad započinjemo uvođenjem osnovnih geometrijskih pojmova potrebnih za razradu Miquelovog teorema. Nakon iskaza, prezentiramo detaljan i precizan dokaz Miquelovog teorema. U ostatku rada detaljnije proučavamo Miquelovu točku, Miquelovu kružnicu i Miquelov trokut te neka njihova svojstva i medusobne odnose. Proučavamo generalizaciju Neubergovog teorema, iskazujemo i dokazujemo Simsonov teorem te definiramo Simsonov pravac. Rad završavamo interestantnim pregledom nekih generalizacija Miquelovog teorema na više od tri kružnice.

Abstract (english)

In this thesis, we study Miquel’s theorem and its variants. We begin with an introduction of basic geometric terms essential to develop Miquel’s theorem. After the statement, we present a detailed and precise proof of Miquel’s theorem. In the rest of the thesis, we study Miquelov’s point, Miquel’s circle and Miquel’s triangle in detail and some of their properties and mutual relationships. We study the generalization of Neuberg’s theorem, state and prove Simson’s theorem and define Simson’s line. At the end of the thesis, we present an interesting overview of some generalizations of Miquel’s theorem on more than three circles.

• Keywords: Miquelova točka; Miquelova kružnica; Miquelov trokut; Neubergov teorem; Simsonov teorem
• Language: croatian
• URN:NBN: urn:nbn:hr:217:243927
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: sveučilišni magistar edukacije matematike (sveučilišni magistar edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2024-03-14 10:56:13