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master's thesis
Miquelov teorem
Zagreb: University of Zagreb, Faculty of Science, 2024. urn:nbn:hr:217:243927
Novosel, Tena
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

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Novosel, T. (2024). Miquelov teorem (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:243927

Novosel, Tena. "Miquelov teorem." Master's thesis, University of Zagreb, Faculty of Science, 2024. https://urn.nsk.hr/urn:nbn:hr:217:243927

Novosel, Tena. "Miquelov teorem." Master's thesis, University of Zagreb, Faculty of Science, 2024. https://urn.nsk.hr/urn:nbn:hr:217:243927

Novosel, T. (2024). 'Miquelov teorem', Master's thesis, University of Zagreb, Faculty of Science, accessed 26 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:243927

Novosel T. Miquelov teorem [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2024 [cited 2024 November 26] Available at: https://urn.nsk.hr/urn:nbn:hr:217:243927

T. Novosel, "Miquelov teorem", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2024. Available at: https://urn.nsk.hr/urn:nbn:hr:217:243927

Metadata
TitleMiquelov teorem
Title (english)Miquel's theorem
AuthorTena Novosel
MentorMarija Galić (mentor)
Committee memberMarija Galić (predsjednik povjerenstva)
Committee memberAleksandra Čižmešija (član povjerenstva)
Committee memberDražen Adamović (član povjerenstva)
Committee memberMatko Ljulj (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2024-02-28, 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
Languagecroatian
URN:NBNurn:nbn:hr:217:243927
Study programmeTitle: 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 resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2024-03-14 10:56:13