Baricentričke koordinate 20 centara trokuta

master's thesis

• Author: Željka Ćaćić
• Mentor: Vjekoslav Kovač (mentor)
• Committee member: Vjekoslav Kovač (predsjednik povjerenstva)
• Committee member: Juraj Šiftar (član povjerenstva)
• Committee member: Boris Guljaš (član povjerenstva)
• Committee member: Zvonko Iljazović (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2017-02-23, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom su radu izvedene baricentričke koordinate 20 centara trokuta koji se nalaze u enciklopediji ETC, krenuvši od klasičnih karakterističnih točaka trokuta do nekih manje poznatih. Baricentričke koordinate određuju položaj proizvoljne točke u ravnini obzirom na trokut, a kako bi se one izračunale, korišteni su brojni teoremi i poučci o trokutu, od jednostavnijih, kao što su poučci o sličnosti i sukladnosti trokuta, pa do složenijih i manje poznatih poput primjerice Van Aubelovog teorema. Također, rad sadrži brojne slike za lakše praćenje dokaza, koje su sve izrađene programskim paketom GeoGebra.

Abstract (english)

In this thesis, barycentric coordinates of 20 triangle centers from the encyclopedia ETC are calculated, starting with the classical centers, and ending up with some less known ones. Barycentric coordinates determine the position of an arbitrary point in the plane with respect to the triangle, and in order to calculate them, numerous theorems and claims about a triangle were used, from the simple ones, like the theorems about congruence and similarity, to the more complex ones, like Van Aubel’s theorem. Moreover, the thesis contains numerous illustrations intended to aid reading of the proofs, which were all drawn using the program package GeoGebra.

• Keywords: baricentričke koordinate; GeoGebra; centri trokuta
• Keywords (english): barycentric coordinates; GeoGebra; triangle centers
• Language: croatian
• URN:NBN: urn:nbn:hr:217:220389
• 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: 2017-04-20 10:05:54