Značajni pravci u geometriji trokuta

Alilović, Mirta

prikaz prve stranice dokumenta Značajni pravci u geometriji trokuta

Download
PDF 1.97 MB

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

Cite this document

APA 6th Edition

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

MLA 8th Edition

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

Chicago 17th Edition

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

Harvard

Alilović, M. (2018). 'Značajni pravci u geometriji trokuta', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 03 December 2024, https://urn.nsk.hr/urn:nbn:hr:126:883290

Vancouver

Alilović M. Značajni pravci u geometriji trokuta [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2018 [cited 2024 December 03] Available at: https://urn.nsk.hr/urn:nbn:hr:126:883290

IEEE

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

Cite this item: https://urn.nsk.hr/urn:nbn:hr:126:883290

Please login to the repository to save this object to your list.

Metadata

Title	Značajni pravci u geometriji trokuta
Title (english)	Significant Lines in Geometry of a Triangle
Author	Mirta Alilović
Mentor	Zdenka Kolar-Begović (mentor)
Mentor	Ljiljana Primorac Gajčić (komentor)
Committee member	Mihaela Ribičić Penava (predsjednik povjerenstva)
Committee member	Zdenka Kolar-Begović (član povjerenstva)
Committee member	Tomislav Marošević (član povjerenstva)
Granter	Josip 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 country	2018-03-20, 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)
Language	croatian
URN:NBN	urn:nbn:hr:126:883290
Study programme	Title: 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 resource	Text
File origin	Born digital
Access conditions	Open access
Terms of use
Repository	Repository of School of Applied Mathematics and Informatics
Created on	2018-03-21 10:37:24