Otkrivanje kolinearnosti karakterističnih točaka trokuta programom GeoGebra

master's thesis

• Author: Ivana Kladić
• Mentor: Vjekoslav Kovač (mentor)
• Committee member: Mea Bombardelli (predsjednik povjerenstva)
• Committee member: Marcela Hanzer (član povjerenstva)
• Committee member: Vanja Wagner (član povjerenstva)
• Committee member: Boris Muha (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2019-11-27, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom diplomskom radu promatrali smo 20 karakterističnih točaka trokuta. Neke su više poznate kao što su središte upisane kružnice, težište, središte opisane kružnice te ortocentar, dok su druge nešto manje poznate. Potom smo te točke unijeli u radnu bilježnicu programa GeoGebra i na taj način vizualno detektirali potencijalne skupove međusobno kolinearnih točaka među njima. Jedan od pravaca na kojem leže neke od karakterističnih točaka trokuta je i čuveni Eulerov pravac. Na kraju smo uočene kolinearnosti rigorozno dokazali koristeći elementarne metode euklidske geometrije.

Abstract (english)

In this thesis we have discussed 20 triangle centers. Some of them are better known than the others, such as incenter, centroid, circumcenter and orthocenter. We than entered these centers into a GeoGebra workbook and that allowed us to visually detect potential sets of mutually collinear points among them. One of the lines that passes through some of the triangle centers is the famous Euler line. Finally, we have rigorously proved observed collinearities using elementary methods of Euclidean geometry.

• Keywords: trokut; karakteristične točke trokuta; kolinearnost; Eulerov pravac
• Keywords (english): triangle; triangle centers; collinearity; Euler line
• Language: croatian
• URN:NBN: urn:nbn:hr:217:680939
• Study programme: Title: 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 resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2020-07-03 11:36:54