Obla geometrijska tijela u školskoj matematici

master's thesis

• Author: Lea Golubić
• 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

Rad je podijeljen u četiri poglavlja. Prvo poglavlje govori o povijesti oblih geometrijskih tijela te kako se ona uvode u školsku matematiku. Također je objašnjen Cavalierijev princip računanja obujma te je spomenuta kratka povijest broja \(\pi\) s obzirom da se on pojavljuje u formulama za oplošje i obujam oblih geometrijskih tijela. U svakom od sljedećih poglavlja opisano je jedno oblo geometrijsko tijelo te kako je ono uvedeno u osnovnu, odnosno srednju školu. Tako je drugo poglavlje posvećeno valjku, u trećem poglavlju je riječ o stošcu, dok se u posljednjem poglavlju govori o kugli i sferi. Osim definicija pojedinih geometrijskih tijela, izvedene su osnovne formule za oplošje i obujam te su objašnjeni zadaci koji su se javili na školskom, županijskom ili državnom natjecanju posljednjih 10 godina.

Abstract (english)

This thesis is divided into four chapters. The first chapter is devoted to the history of oblique geometric solids and how they are introduced into school. There was also explained Cavalier’s Principle for Volume and the short history of the number \(\pi\) because it appears in the surface area and the volume of oblique geometric solids. Each of the following chapters describes one oblique geometric solid and how it is introduced into primary and secondary school. The second chapter is dedicated to the cylinder, in the third chapter it is a cone, while in the last chapter it is about the sphere. In addition to the definitions of individual geometric solids, basic formulas for surface area and volume have been introduced and the tasks that have occurred at school, county or state competition for the past 10 years have been explained.

• Keywords: obla geometrijska tijela; nastava matematike; matematička natjecanja
• Keywords (english): oblique geometric solids; teaching mathematics; mathematical competitions
• Language: croatian
• URN:NBN: urn:nbn:hr:217:890868
• 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: 2020-01-24 12:43:50