Karakterizacije parabole

master's thesis

• Author: Marko Saratlija
• Mentor: Juraj Šiftar (mentor)
• Committee member: Juraj Šiftar (predsjednik povjerenstva)
• Committee member: Vedran Krčadinac (član povjerenstva)
• Committee member: Vlado Volenec (član povjerenstva)
• Committee member: Nela Bosner (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2014-09-24, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom diplomskom radu iskazano je i dokazano desetak karakterizacija parabole. Za većinu tih svojstava dobro je poznato, čak i iz antičkih vremena, da ih parabola posjeduje, no manje je poznato da su ta svojstva medu ravninskim krivuljama karakteristična upravo za parabolu. Pritom parabolu promatramo kao graf diferencijabilne funkcije s određenim geometrijskim svojstvima. Stoga se u dokazima, uz geometrijska razmatranja, koriste i razni rezultati iz matematičke analize. Iskazane tvrdnje popraćene su nizom ilustracija koje uvelike olakšavaju razumijevanje sadržaja.

Abstract (english)

In this graduate thesis a dozen characterizations of parabola are presented and proven. For most of these properties it is well known, even from ancient times, that a parabola possesses them, but it is less known that these properties are characteristic among planar curves just for the parabola. The parabola is viewed as a graph of a differentiable function with specific geometric properties. Therefore, in proofs, along with geometric considerations, various results of mathematical analysis are used, too. Furthermore, our statements are accompanied by a series of illustrations that greatly facilitate understanding of the content.

• Keywords: karakterizacija parabole; parabola kao graf diferencijabilne funkcije s određenim geometrijskim svojstvima
• Keywords (english): characterizations of parabola; parabola as a graph of a differentiable function
• Language: croatian
• URN:NBN: urn:nbn:hr:217:203812
• Study programme: Title: Mathematical Statistics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Access restricted to students and staff of home institution
• Created on: 2019-02-06 13:52:20