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master's thesis
Platonova tijela
Zagreb: University of Zagreb, Faculty of Science, 2019. urn:nbn:hr:217:926243
Pantaler, Melita
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Pantaler, M. (2019). Platonova tijela (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:926243

Pantaler, Melita. "Platonova tijela." Master's thesis, University of Zagreb, Faculty of Science, 2019. https://urn.nsk.hr/urn:nbn:hr:217:926243

Pantaler, Melita. "Platonova tijela." Master's thesis, University of Zagreb, Faculty of Science, 2019. https://urn.nsk.hr/urn:nbn:hr:217:926243

Pantaler, M. (2019). 'Platonova tijela', Master's thesis, University of Zagreb, Faculty of Science, accessed 03 July 2024, https://urn.nsk.hr/urn:nbn:hr:217:926243

Pantaler M. Platonova tijela [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2019 [cited 2024 July 03] Available at: https://urn.nsk.hr/urn:nbn:hr:217:926243

M. Pantaler, "Platonova tijela", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2019. Available at: https://urn.nsk.hr/urn:nbn:hr:217:926243

Metadata
TitlePlatonova tijela
AuthorMelita Pantaler
MentorDora Pokaz (mentor)
MentorSanja Varošanec (mentor)
Committee memberDora Pokaz (predsjednik povjerenstva)
Committee memberSanja Varošanec (član povjerenstva)
Committee memberSonja Štimac (član povjerenstva)
Committee memberMarko Erceg (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2019-09-23, 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
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:926243
Study programmeTitle: 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 resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2020-02-14 14:05:01