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master's thesis
Točke ekstrema nekih geometrijskih izraza vezanih uz trokut
Zagreb: University of Zagreb, Faculty of Science, 2020. urn:nbn:hr:217:417654
Kolić, Marija
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Kolić, M. (2020). Točke ekstrema nekih geometrijskih izraza vezanih uz trokut (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:417654

Kolić, Marija. "Točke ekstrema nekih geometrijskih izraza vezanih uz trokut." Master's thesis, University of Zagreb, Faculty of Science, 2020. https://urn.nsk.hr/urn:nbn:hr:217:417654

Kolić, Marija. "Točke ekstrema nekih geometrijskih izraza vezanih uz trokut." Master's thesis, University of Zagreb, Faculty of Science, 2020. https://urn.nsk.hr/urn:nbn:hr:217:417654

Kolić, M. (2020). 'Točke ekstrema nekih geometrijskih izraza vezanih uz trokut', Master's thesis, University of Zagreb, Faculty of Science, accessed 06 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:417654

Kolić M. Točke ekstrema nekih geometrijskih izraza vezanih uz trokut [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2020 [cited 2024 December 06] Available at: https://urn.nsk.hr/urn:nbn:hr:217:417654

M. Kolić, "Točke ekstrema nekih geometrijskih izraza vezanih uz trokut", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2020. Available at: https://urn.nsk.hr/urn:nbn:hr:217:417654

Metadata
TitleTočke ekstrema nekih geometrijskih izraza vezanih uz trokut
Title (english)Extreme points of some geometric expressions related to a triangle
AuthorMarija Kolić
MentorVjekoslav Kovač (mentor)
Committee memberVjekoslav Kovač (predsjednik povjerenstva)
Committee memberHrvoje Šikić (član povjerenstva)
Committee memberZoran Vondraček (član povjerenstva)
Committee memberDijana Ilišević (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2020-09-29, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom diplomskom radu promatrali smo neke od najpoznatijih primjera geometrijskih izraza vezanih uz trokut i njihove minimalne, odnosno maksimalne vrijednosti po svim točkama trokuta. U prve dvije tvrdnje rada kao točke ekstrema smo nalazili težište, kao jednu od najučestalijih točaka trokuta, dok su se u preostale dvije tvrdnje ekstremi postizali u ne tako poznatim točkama trokuta što se tiče sustava osnovnoškolskog i srednjoškolskog obrazovanja. Najprije smo svaku od tih točaka, odnosno težište, Fermatovu točku te Lemoineovu točku, definirali i opisali njihova svojstva, dok smo potom svaku od glavnih tvrdnji ovoga rada, odnosno teoreme o ekstremima geometrijskih izraza vezanih uz trokut iskazali i detaljno dokazali. Na kraju smo svaku od tvrdnji ilustrirali u programu GeoGebra i na taj način vizualno potkrijepili prethodne dokaze u svrhu jednostavnijeg razumijevanja i otkrivanja danih tvrdnji za same učenike.
Abstract (english)
In this thesis, we have observed some of the best known examples of geometric expressions related to the triangle and their minimum and maximum values over all points of the triangle. In the first two statements of this work the extreme points are found to be the centroid, which is one of the most frequent points of the triangle, while in the remaining two statements the extremes were achieved in not so well known points of the triangle, as far as the primary and secondary education systems are concerned. First, we defined and described each of these points and their properties, i.e., the centroid, the Fermat point and the Lemoine point, and then we stated and proved in detail each of the main statements of this paper, that is the theorems on the extremes of geometric expressions related to a triangle. Finally, we illustrated each of the claims in the GeoGebra program and thus visually enhanced the previous proofs for the purpose of easier understanding and discovery of the given claims by students on their own
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:417654
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 on2021-02-26 12:30:37