Primjena vektorske metode

master's thesis

• Author: Karlo Markić
• Mentor: Sanja Varošanec (mentor)
• Committee member: Sanja Varošanec (predsjednik povjerenstva)
• Committee member: Boris Guljaš (član povjerenstva)
• Committee member: Matija Kazalicki (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2017-09-27, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu opisujemo vektorsku metodu te pomoću nje dokazujemo mnoge dobro poznate planimetrijske i stereometrijske probleme. Rad je podijeljen na osam poglavlja. U prvom poglavlju donosimo pregled osnovnih definicija i tvrdnji vezanih uz vektore i vektorski račun. U drugom poglavlju definiramo radijvektor točke u ravnini i prostoru te dokazujemo geometrijske tvrdnje koristeći radijvektore. U trećem, četvrtom i petom poglavlju definiramo operacije skalarnog, vektorskog i mješovitog množenja, dokazujemo njihova bitna svojstva te iskazujemo neke posljedice tih svojstava. Primjenom definicija i svojstava ovih operacija dokazujemo mnoge tvrdnje iz elementarne geometrije. Posljednja tri poglavlja su posvećena primjeni vektorske metode na trokut, četverokut i kružnicu te tetraedar, paralelepiped i sferu.

Abstract (english)

In this thesis, we describe the vector method and we prove many well-known planimetric and stereometric problems by using it. Thesis is divided into eight chapters. In the first chapter, we provide an overview of basic definitions and claims related to vectors and operations on them. In the second chapter, we define radius vectors in the plane and in the space and we prove some planimetric problems by applying them. In the third, the fourth and the fifth chapter, we define the inner, vector (cross) and mixed (scalar triple) products of vectors. We also apply these operations to solve some geometric problems. In last three chapters, we show the application of the vector method to triangle, quadrilateral, circle, tetrahedron, parallelepiped and sphere.

• Keywords: vektori; vektorska metoda; vektroski račun; radijvektor; trokut; četverokut; kružnica; tetraedar; paralelepiped; sfera
• Keywords (english): vectors; operations on vectors; vector method; radius vectors; triangle; quadrilateral; circle; tetrahedron; parallelepiped; sphere
• Language: croatian
• URN:NBN: urn:nbn:hr:217:808789
• 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: 2018-02-28 11:30:20