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master's thesis
Primjena koordinatne metode u planimetriji
Zagreb: University of Zagreb, Faculty of Science, 2018. urn:nbn:hr:217:545967
Barać, Katarina
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Barać, K. (2018). Primjena koordinatne metode u planimetriji (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:545967

Barać, Katarina. "Primjena koordinatne metode u planimetriji." Master's thesis, University of Zagreb, Faculty of Science, 2018. https://urn.nsk.hr/urn:nbn:hr:217:545967

Barać, Katarina. "Primjena koordinatne metode u planimetriji." Master's thesis, University of Zagreb, Faculty of Science, 2018. https://urn.nsk.hr/urn:nbn:hr:217:545967

Barać, K. (2018). 'Primjena koordinatne metode u planimetriji', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:545967

Barać K. Primjena koordinatne metode u planimetriji [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2018 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:545967

K. Barać, "Primjena koordinatne metode u planimetriji", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2018. Available at: https://urn.nsk.hr/urn:nbn:hr:217:545967

Metadata
TitlePrimjena koordinatne metode u planimetriji
AuthorKatarina Barać
MentorSanja Varošanec (mentor)
Committee memberSanja Varošanec (predsjednik povjerenstva)
Committee memberGoran Radunović (član povjerenstva)
Committee memberMladen Vuković (član povjerenstva)
Committee memberZvonko Iljazović (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2018-11-27, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu opisujemo koordinatnu metodu u planimetriji te pomoću nje dokazujemo razne teoreme iz različitih područja matematike. Na samom početku definiran je koordinatni sustav na pravcu i koordinatni sustav u ravnini te je dana kratka povijesna crtica o nastanku Kartezijevog koordinatnog sustava. Definirali smo i koordinatnu metodu. Navedeni su i osnovni teoremi analitičke geometrije koje ćemo koristiti u radu. Teoreme o četiri karakteristične točke trokuta (težište, ortocentar, središte opisane kružnice, središte upisane kružnice) te teorem o Eulerovom pravcu smo dokazali koordinatnom metodom. Prikazali smo i zadatke s matematičkih natjecanja na kojima je moguća primjena koordinatne metode. Teoreme o trokutu i četverokutu također smo dokazali koordinatnom metodom. Na kraju smo naveli neka svojstva krivulja drugog reda, tj. svojstva elipse, hiperbole i parabole te ih dokazali primjenjujući koordinatnu metodu.
Abstract (english)
In this thesis, the coordinate method in planimetry is described and it is used to prove several theorems from various fields of mathematics. At the beginning of the paper the Cartesian coordinate system on line and on plane are defined, and the short history overview of the Cartesian coordinate system is mentioned. The coordinate method is defined. The basic theorems of analytic geometry are also mentioned. Theorems of triangle concurrency points (centroid, orthocenter, circumcenter, incenter) and Euler line theorem are proved with coordinate method. Mathematical competition problems where application of coordinate method is possible are shown. Theorems of the triangle and quadrilateral are also proved with coordinate method. At the end of this thesis, some properties of the second-order curves, i. e. properties of ellipse, hyperbola, parabola are shown and proved with coordinate method.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:545967
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 on2019-03-04 09:59:02