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master's thesis
Značajni pravci u geometriji trokuta
Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2018. urn:nbn:hr:126:883290
Alilović, Mirta
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Applied Mathematics and Computer Science
Applied Mathematics and Optimization Research Group

Institutional repository: Repository of School of Applied Mathematics and Informatics

Cite this document

Alilović, M. (2018). Značajni pravci u geometriji trokuta (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:883290

Alilović, Mirta. "Značajni pravci u geometriji trokuta." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2018. https://urn.nsk.hr/urn:nbn:hr:126:883290

Alilović, Mirta. "Značajni pravci u geometriji trokuta." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2018. https://urn.nsk.hr/urn:nbn:hr:126:883290

Alilović, M. (2018). 'Značajni pravci u geometriji trokuta', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 21 December 2024, https://urn.nsk.hr/urn:nbn:hr:126:883290

Alilović M. Značajni pravci u geometriji trokuta [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2018 [cited 2024 December 21] Available at: https://urn.nsk.hr/urn:nbn:hr:126:883290

M. Alilović, "Značajni pravci u geometriji trokuta", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2018. Available at: https://urn.nsk.hr/urn:nbn:hr:126:883290

Metadata
TitleZnačajni pravci u geometriji trokuta
Title (english)Significant Lines in Geometry of a Triangle
AuthorMirta Alilović
MentorZdenka Kolar-Begović (mentor)
MentorLjiljana Primorac Gajčić (komentor)
Committee memberMihaela Ribičić Penava (predsjednik povjerenstva)
Committee memberZdenka Kolar-Begović (član povjerenstva)
Committee memberTomislav Marošević (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Applied Mathematics and Computer Science)
(Applied Mathematics and Optimization Research Group)
Osijek
Defense date and country2018-03-20, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Geometry and Topology
Abstract
Eulerov pravac trokuta je pravac na kojem leže ortocentar, težište i središte trokutu opisane kružnice. U literaturi postoje brojni dokazi tvrdnje o kolinearnosti ove tri točke trokuta. U ovom diplomskom radu predstavljen je dokaz pomoću vektora i dokaz korištenjem homotetije. Razmatrana je veza Eulerovog pravca i Eulerove kružnice trokuta. Dokazane su tvrdnje o vezama između ovih pojmova. Simsonov, odnosno Wallaceov pravac trokuta je pravac na kojem leže nožišta okomica povučenih iz neke točke na trokutu opisanoj kružnici na stranice tog trokuta. U radu je dokazana tvrdnja o spomenutoj kolinearnosti nožišta okomica. Dokazan je i niz tvrdnji o različitim svojstvima ovog pravca te istražene veze s Eulerovom kružnicom trokuta.
Abstract (english)
The orhocenter, the centroid of a triangle and the center of the circumscribed circle of a triangle lie on one line, the so called Euler line. The proof of this statement is given in this work. The properties of Euler line are also considered, especially the connection between the Euler line and the Euler circle of a triangle. The feet of the perpendiculars to the sides of triangle from a point on its circumscribed circle are collinear. This line is called Simson (Simson-Wallace) line. A number of statements about this concept is proved. The connection between Simson line and Euler circle is also considered in this work.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:883290
Study programmeTitle: Mathematics and Computer Science
Study programme type: university
Study level: integrated undergraduate and 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
Terms of useLicence In copyright icon
Created on2018-03-21 10:37:24