Točke trokuta s ekstremalnim svojstvima

master's thesis

• Title (english): Points of a triangle with extremal properties
• Author: Danka Bradarić
• Mentor: Sanja Varošanec (mentor)
• Committee member: Sanja Varošanec (predsjednik povjerenstva)
• Committee member: Goran Radunović (član povjerenstva)
• Committee member: Marko Radulović (član povjerenstva)
• Committee member: Marcela Hanzer (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2022-09-28, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom su diplomskom radu navedeni neki primjeri točaka trokuta za koje odredene funkcije postižu svoju minimalnu ili maksimalnu vrijednost. Tako su se ekstremi raznih funkcija postizali u četiri karakteristične točke trokuta - težištu, ortocentru, središtu upisane i opisane kružnice, ali i u drugim točkama trokuta koje nisu sastavni dio kurikuluma nastavnog predmeta Matematike u osnovnim i srednjim školama poput Fermat-Torricellijeve točke, Lemoineove točke te središta trokutu pripisanih kružnica. Te su točke u radu definirane te su navedena i dokazana neka njihova posebna svojstva.

Abstract (english)

In this thesis, some examples of triangle points for which certain functions reach their minimum or maximum value are given. Thus, it could be seen that the extremal values of various functions were reached in the four characteristic points of the triangle - the centroid, the orthocenter, the center of the inscribed and circumscribed circle, but also in other points of the triangle that are not an integral part of the curriculum of the subject of Mathematics in primary and secondary schools, such as the Fermat-Torricelli point, the Lemoine point and the excentres. These points were defined and some of their special properties were stated and proven.

• Keywords: trokut; težište; ortocentar; središte opisane kružnice trokuta; središte upisane kružnice trokuta; središte pripisane kružnice trokuta; simedijane; Lemoineova točka; Fermat-Torricellijeva točka; ekstremi
• Keywords (english): triangle; centroid; orthocentre; circumcentre; incentre; excentre; symmedians; Lemoine point; Fermat-Torricelli point; extrema
• Language: croatian
• URN:NBN: urn:nbn:hr:217:928891
• Study programme: Title: Mathematics and Computer Science Education; specializations in: Mathematics and Computer Science Education; Course: Mathematics and Computer Science Education; Study programme type: university; Study level: 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
• Created on: 2022-10-24 12:12:46