Težišnice trokuta i težište

master's thesis

• Author: Tonio Škaro
• Mentor: Sanja Varošanec (mentor)
• Committee member: Sanja Varošanec (predsjednik povjerenstva)
• Committee member: Mirko Primc (član povjerenstva)
• Committee member: Mirko Polonijo (član povjerenstva)
• Committee member: Aleksandra Čižmešija (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2015-09-24, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Težišnice trokuta, kao i težište, su zaista posebne veličine koje svaki trokut posjeduje. Tijekom povijesti su ih matematičari promatrali te su donijeli neke zaključke o njima koji su im pomogli razumjeti neke posebne odnose u svakom trokutu. Svojstva koja smo dokazali na više načina omogućuju i ne tako vrsnim matematičarima da razumiju kakvi odnosi u trokutu vrijede i zašto se baš na neki određeni način mora koristiti pojedinim elementima kako bi došli do rješenja. U svakom slučaju, težišnice trokuta, kao dužine koje spajaju jedan vrh sa polovištem nasuprotne stranice u trokutu, i težište trokuta, kao geometrijsko mjesto točaka u kojemu se sve tri težišnice sijeku, su zaista posebne veličine vrijedne promatranja koje nam pomažu u razumijevanju odnosa u trokutima.

Abstract (english)

Medians of a triangle, as well as the centroid of a triangle, geometrically speaking, are some really special parts that every triangle has. Through history, they have been object of observation by many mathematicians who have come to useful conclusions about them. Those conclusions have been used in understanding some specific relations in every triangle. Because of all those established properties, people who are not that good in mathematics can easily understand which relations in a triangle are valid and why some specific elements must be used in a certain way in order to come to not so easily obtainable solutions. Anyhow, medians of a triangle defined as line segments from vertices to the midpoints of the opposite sides, and the centroid as the intersection point of meridians, are parts of a triangle worth observing that help us understand specific relations in every triangle.

• Keywords: težišnice trokuta; težište trokuta; razumijevanje odnosa u trokutima
• Keywords (english): medians of a triangle; centroid of a triangle; understanding of specific relations in every triangle
• Language: croatian
• URN:NBN: urn:nbn:hr:217:959407
• 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: 2019-02-13 11:46:36