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master's thesis
Baricentrične koordinate - primjena na geometriju trokuta
Zagreb: University of Zagreb, Faculty of Science, 2023. urn:nbn:hr:217:624163
Klarin, Tina
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Klarin, T. (2023). Baricentrične koordinate - primjena na geometriju trokuta (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:624163

Klarin, Tina. "Baricentrične koordinate - primjena na geometriju trokuta." Master's thesis, University of Zagreb, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:217:624163

Klarin, Tina. "Baricentrične koordinate - primjena na geometriju trokuta." Master's thesis, University of Zagreb, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:217:624163

Klarin, T. (2023). 'Baricentrične koordinate - primjena na geometriju trokuta', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:624163

Klarin T. Baricentrične koordinate - primjena na geometriju trokuta [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2023 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:624163

T. Klarin, "Baricentrične koordinate - primjena na geometriju trokuta", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2023. Available at: https://urn.nsk.hr/urn:nbn:hr:217:624163

Metadata
TitleBaricentrične koordinate - primjena na geometriju trokuta
Title (english)Baricentrične koordinate - primjena na geometriju trokuta
AuthorTina Klarin
MentorMea Bombardelli (mentor)
Committee memberMea Bombardelli (predsjednik povjerenstva)
Committee memberVjekoslav Kovač (član povjerenstva)
Committee memberMarcela Hanzer (član povjerenstva)
Committee memberSnježana Lubura Strunjak (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2023-03-03, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Baricentrične koordinate vrsta su homogenih koordinata koje se pridružuju točki ravnine s obzirom na referentni trokut sustava. Baricentrične koordinate možemo definirati pomoću vektorskog računa ili pomoću orijentiranih površina i orijentiranih duljina što se može vidjeti u prvom dijelu ovog rada. Karakteristično svojstvo jednadžbe pravca i kružnice u baricentričnom koordinatnom sustavu je homogenost što nam uvelike olakšava njihovo određivanje i računanje njima. Budući da je upravo trokut referentni sustav baricentričnog koordinatnog sustava, baricentrične koordinate pokazuje se pogodnim izborom u dokazivanju teorema i rješavanju zadataka geometrije trokuta. U drugom poglavlju ovog rada iskazani su i dokazani neki poznati teoremi i tvrdnje geometrije trokuta, a u trećem je poglavlju koordinatnom metodom riješeno nekoliko zadataka s matematičkih natjecanja.
Abstract (english)
Barycentric coordinates are a type of homogeneous coordinates that join a point of the plane with respect to the reference triangle of the system. We can define barycentric coordinates using vector calculus or using oriented surfaces and oriented lengths, which can be seen in the first part of this paper. A characteristic property of the equation of a line and a circle in the barycentric coordinate system is homogeneity, which greatly facilitates their determination and calculation. Since the triangle is the reference system of the barycentric coordinate system, barycentric coordinates prove to be a suitable choice for proving theorems and solving triangle geometry problems. In the second chapter of this paper, some well-known theorems and claims of triangle geometry are presented and proven, and in the third chapter, several problems from mathematical competitions are solved using the coordinate method.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:624163
Study programmeTitle: Mathematics Education; specializations in: Mathematics Education
Course: Mathematics Education
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2023-07-25 13:48:25