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master's thesis
Upisana i pripisane kružnice trokuta
Zagreb: University of Zagreb, Faculty of Science, 2019. urn:nbn:hr:217:292956
Bešenić, Anamarija
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

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Bešenić, A. (2019). Upisana i pripisane kružnice trokuta (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:292956

Bešenić, Anamarija. "Upisana i pripisane kružnice trokuta." Master's thesis, University of Zagreb, Faculty of Science, 2019. https://urn.nsk.hr/urn:nbn:hr:217:292956

Bešenić, Anamarija. "Upisana i pripisane kružnice trokuta." Master's thesis, University of Zagreb, Faculty of Science, 2019. https://urn.nsk.hr/urn:nbn:hr:217:292956

Bešenić, A. (2019). 'Upisana i pripisane kružnice trokuta', Master's thesis, University of Zagreb, Faculty of Science, accessed 22 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:292956

Bešenić A. Upisana i pripisane kružnice trokuta [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2019 [cited 2024 November 22] Available at: https://urn.nsk.hr/urn:nbn:hr:217:292956

A. Bešenić, "Upisana i pripisane kružnice trokuta", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2019. Available at: https://urn.nsk.hr/urn:nbn:hr:217:292956

Metadata
TitleUpisana i pripisane kružnice trokuta
AuthorAnamarija Bešenić
MentorMea Bombardelli (mentor)
Committee memberMea Bombardelli (predsjednik povjerenstva)
Committee memberMario Novak (član povjerenstva)
Committee memberRobert Manger (član povjerenstva)
Committee memberMaja Resman (član povjerenstva)
Committee memberDanko Radić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2019-02-28, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu proučavali smo trokut, njemu pridružene kružnice te njihova središta. Promatrali smo sličnosti, veze i svojstva između njih. Uz četiri najpoznatije karakteristične točke trokuta: težište, ortocentar, središte trokutu upisane kružnice i središte trokutu opisane kružnice, osvrnuli smo se i na druge, manje poznate karakteristične točke trokuta poput Gergonnove točke i Nagelove točke. Također, proučavali smo metričke relacije među karakterističnim točkama. Nadalje, definirali smo Feuerbachovu kružnicu i pokazali njezina svojstva. Na samom kraju rada dokazali smo jedan od najljepših teorema geometrije trokuta: Feuerbachov teorem koji govori da Feuerbachova kružnica dira upisanu kružnicu danog trokuta iznutra, a njegove pripisane kružnice izvana.
Abstract (english)
This paper sets out to study the triangle, the circles connected with the triangle, and their centres. In the study, their properties, as well as the similarities and relationships between them, have been observed. Apart from the four points of concurrency in triangles: the centroid, the orthocentre, the incentre and the circumcentre, other, less known concurrency points, such as the Gergonne point and the Nagel point, have also been addressed. Furthermore, the Feuerbach circle has also been defined and its properties have been demonstrated. At the very end of the paper, one of the most beautiful theorems of the triangle geometry, the Feuerbach theorem, which states that the Feuerbach circle is tangent internally to the incircle and tangent externally to the triangles excircles, has been proved.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:292956
Study programmeTitle: 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 resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-07-10 12:07:26