Platonova tijela

master's thesis

• Author: Melita Pantaler
• Mentor: Dora Pokaz (mentor)
• Mentor: Sanja Varošanec (mentor)
• Committee member: Dora Pokaz (predsjednik povjerenstva)
• Committee member: Sanja Varošanec (član povjerenstva)
• Committee member: Sonja Štimac (član povjerenstva)
• Committee member: Marko Erceg (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2019-09-23, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu opisujemo uvođenje Platonovih tijela u školskoj matematici. Na samom početku opisan je Platonov život te je pojašnjeno zašto su pravilni poliedri dobili naziv Platonova tijela. Također su opisane zanimljivosti o pravilnim poliedrima. Definirali smo osnovne pojmove vezane uz pravilne poliedre, dokazali Eulerovu formulu te smo dokazali da postoji točno pet pravilnih poliedara. Objasnili smo na koji način se uvodi Cavalierijev princip računanja obujma na nivou srednje škole. Nakon toga slijedi pregled svih Platonovih tijela kroz osnovnu i srednju školu. Na kraju smo prikazali zadatke s matematičkih natjecanja te ih riješili.

Abstract (english)

In this master’s thesis, the introduction of Platonic solid to school mathematics is described. In the beginning, Plato’s life is described and it is explained why regular polyhedron is called Platonic solid. Afterwards, interesting facts about regular polyhedron are described. Moreover, basic terms related to regular polyhedrons are defined, Euler’s formula is proven and it is proven that there are exactly five regular polyhedrons. We explain how Cavalier’s principle of volume calculation is taught in high school. This is followed by an overview of all Platonic solid through elementary and high school. In the end, problems from mathematical competitions are presented and completely. solved.

• Keywords: Platonova tijela; nastava matematike; pravilni polierdri; Eulerova formula; Cavalierijev princip računanja obujma
• Keywords (english): Platonic solids; teaching mathematics; regular polyhedron; Euler’s formula; Cavalier’s principle of volume calculation
• Language: croatian
• URN:NBN: urn:nbn:hr:217:926243
• 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: 2020-02-14 14:05:01