Opća svojstva konveksnog četverokuta

master's thesis

• Author: Marija Žužul
• Mentor: Mario Krnić (mentor)
• Mentor: Mea Bombardelli (sumentor)
• Committee member: Mario Krnić (predsjednik povjerenstva)
• Committee member: Mea Bombardelli (član povjerenstva)
• Committee member: Zvonimir Bujanović (član povjerenstva)
• Committee member: Vedran Čačić (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

Na početku rada prisjećamo se osnovne podjele četverokuta, temeljnih pojmova i činjenica potrebnih za ostatak rada. U drugom poglavlju bavimo se Eulerovim teoremom koji je poopćenje relacije paralelograma, dajemo formulu za površinu općeg konveksnog četverokuta i proširenje Teorema o kosinusu. Dajemo i poopćenje dobro poznatog Ptolomejevog teorema. U trećem poglavlju definiramo težište i težišnice četverokuta, dajemo iskaz i dokaz Varignonovog teorema i njegove posljedice, te se bavimo drugim osobitim točkama u četverokutu.

Abstract (english)

At the beginning of the paper, we recall the basic classification of the quadrilateral, the basic concepts and facts needed for the rest of the paper. In the second chapter we deal with the Euler’s theorem which is a generalization of the relation of parallelograms, we give a formula for the surface of a general convex quadrilateral and an extension of the cosine theorem. We also give a generalization of the well-known Ptolemy’s theorem. In the third chapter, we define the centroids and the medians of the quadrilateral, give a statement and proof of Varignon’s theorem and its consequences, and deal with other significant points in the quadrilateral.

• Keywords: četverokut; Eulerov teorem; teorem o kosinusu; Ptolomejev teorem; Varignonov teorem
• Keywords (english): quadrilateral; Euler’s theorem; cosine theorem; Ptolemy’s theorem; Varignon’s theorem
• Language: croatian
• URN:NBN: urn:nbn:hr:217:727802
• 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: 2020-07-21 09:00:18