Nekoliko pristupa krivuljama drugog reda

master's thesis

• Author: Danica Govorko
• Mentor: Sanja Varošanec (mentor)
• Committee member: Sanja Varošanec (predsjednik povjerenstva)
• Committee member: Marcela Hanzer (član povjerenstva)
• Committee member: Slaven Kožić (član povjerenstva)
• Committee member: Marko Tadić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2019-09-25, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom diplomskom radu bavimo se različitim pristupima krivuljama drugog reda. Na početku rada naveli smo metričke definicije elipse, hiperbole i parabole. Potom smo krivulje drugog reda definirali na još nekoliko načina: pomoću Papus-Boškovićeve definicije, algebarske definicije te kao presjek stožaste plohe ravninom. Dokazali smo da su navedene definicije ekvivalentne metričkoj definiciji svake od krivulja. U drugom dijelu rada naveli smo svojstva elipse, hiperbole i parabole te ih dokazali koordinatnom metodom. Prikazano je i nekoliko zadataka s matematičkih natjecanja te su odabrani zadatci riješeni koordinatnom metodom.

Abstract (english)

In this thesis, we considered different approaches to the second-order curves. In the first part of the thesis, we gave metric definitions of ellipse, hyperbola and parabola. Then we defined the second-order curves in several other ways using the Pappus-Bošković definition, the algebraic definition, and as intersection of a conical surface. We have proved that the above definitions are equivalent to the metric definition of each of the curves. In the second part of the thesis we stated the properties of an ellipse, hyperbola and parabola and proved them with coordinate method. We also presented several mathematical competitions problems and solved them with coordinate method.

• Keywords: krivulje drugog reda; Papus-Boškovićeva definicija; matematička natjecanja; koordinatna metoda
• Keywords (english): second-order curves; Pappus-Bošković definition; mathematical competitions; coordinate method
• Language: croatian
• URN:NBN: urn:nbn:hr:217:479592
• 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: 2020-01-24 12:56:20