Platonova tijela

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.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