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master's thesis
Feuerbachova točka
Zagreb: University of Zagreb, Faculty of Science, 2015. urn:nbn:hr:217:910999
Mihalic, Maja
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

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Mihalic, M. (2015). Feuerbachova točka (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:910999

Mihalic, Maja. "Feuerbachova točka." Master's thesis, University of Zagreb, Faculty of Science, 2015. https://urn.nsk.hr/urn:nbn:hr:217:910999

Mihalic, Maja. "Feuerbachova točka." Master's thesis, University of Zagreb, Faculty of Science, 2015. https://urn.nsk.hr/urn:nbn:hr:217:910999

Mihalic, M. (2015). 'Feuerbachova točka', Master's thesis, University of Zagreb, Faculty of Science, accessed 04 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:910999

Mihalic M. Feuerbachova točka [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2015 [cited 2024 November 04] Available at: https://urn.nsk.hr/urn:nbn:hr:217:910999

M. Mihalic, "Feuerbachova točka", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2015. Available at: https://urn.nsk.hr/urn:nbn:hr:217:910999

Metadata
TitleFeuerbachova točka
AuthorMaja Mihalic
MentorMea Bombardelli (mentor)
Committee memberMea Bombardelli (predsjednik povjerenstva)
Committee memberMirko Primc (član povjerenstva)
Committee memberFranka Miriam Bruckler (član povjerenstva)
Committee memberMarcela Hanzer (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2015-07-13, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom smo radu dokazali dio poznatog Feuerbachova teorema, odnosno da se Feuerbachova kružnica i upisana kružnica nekog trokuta diraju u Feuerbachovoj točki. Zatim smo Feuerbachovu točku povezali s drugim posebnim točkama trokuta. Naime, promatrali smo je u ulozi anti-Steinerove točke, ortopola, Ponceleove točke te smo uspostavili vezu između Feuerbachove tocke i Eulerove točke simetrije. Na kraju, dana je generalizacija Feuerbachova teorema koja je poznata pod nazivom Treći Fontenèov teorem. Tijekom cijelog rada koristilo se znanje o orijentiranim kutovima koje je uvelike olakšalo većinu danih dokaza.
Abstract (english)
this paper we proved the part of the famous Feuerbach theorem, that is, Feuerbach circle of any triangle is tangent to its incircle at Feuerbach point. Then, we connected Feuerbach point with other special points of the triangle. In fact, we have observed it in the role of anti-Steiner point, orthopole, Poncelet point and we have established a relation between Feuerbach point and Euler reflection point. Finally, a generalization of Feuerbach theorem which is known as the Third Fontène theorem is given. Through the entire paper the knowledge of directed angles was used which made many of proofs easier.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:910999
Study programmeTitle: Mathematics and Computer Science Education; specializations in: Mathematics and Computer Science Education
Course: Mathematics and Computer Science Education
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra edukacije matematike i informatike (magistar/magistra edukacije matematike i informatike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
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Created on2019-01-23 12:06:29