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master's thesis
Mjera kuta
Zagreb: University of Zagreb, Faculty of Science, 2014. urn:nbn:hr:217:273919
Capan, Antonija
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Capan, A. (2014). Mjera kuta (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:273919

Capan, Antonija. "Mjera kuta." Master's thesis, University of Zagreb, Faculty of Science, 2014. https://urn.nsk.hr/urn:nbn:hr:217:273919

Capan, Antonija. "Mjera kuta." Master's thesis, University of Zagreb, Faculty of Science, 2014. https://urn.nsk.hr/urn:nbn:hr:217:273919

Capan, A. (2014). 'Mjera kuta', Master's thesis, University of Zagreb, Faculty of Science, accessed 26 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:273919

Capan A. Mjera kuta [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2014 [cited 2024 December 26] Available at: https://urn.nsk.hr/urn:nbn:hr:217:273919

A. Capan, "Mjera kuta", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2014. Available at: https://urn.nsk.hr/urn:nbn:hr:217:273919

Metadata
TitleMjera kuta
AuthorAntonija Capan
MentorZvonko Iljazović (mentor)
Committee memberZvonko Iljazović (predsjednik povjerenstva)
Committee memberMaja Starčević (član povjerenstva)
Committee memberZvonimir Tutek (član povjerenstva)
Committee memberMirko Primc (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2014-07-14, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Rad smo podijelili na 4 cjeline u kojima razrađujemo potrebne pojmove za izgradnju mjere kuta. U prvom poglavlju izgrađujemo pojmove ravnine koju kasnije gledamo kao okolinu za proučavanje kutova. Pritom koristimo Aksiome incidencije te relaciju linearnog uređaja sa različitim svojstvima za izgradnju pojedine vrste ravnine. U drugom poglavlju definiramo pojmove izometrije i osne simetrije i uvodimo pojam apsolutne ravnine kao osnove za daljni rad. Koristimo Osnovni teorem o izometrijama te definiramo rotacije i centralnu simetriju. U trećem poglavlju definiramo pojam neorijentiranog kuta pri čemu nam nul - kut i ispruženi kut čine osnovu za uspoređivanje. Gledamo odnose medu kutovima i uvodimo relaciju ≤ kao sredstvo uspoređivanja. Osim toga, definiramo supremum i infimum te zbroj kutova te na kraju precizno definiramo pojam mjere kuta čije postojanje dokazujemo teoremom.
Abstract (english)
We divided this thesis into 4 major parts. In first chapter we are developing terms of different types of planes as a base for our study of measure of an angle. We are using Axiom of incidence and equivalence relation with different characteristic. In second chapter we define notions as isometry and reflection across a line. Also, we define the notion of an absolute plane. We use Fundamental theorem about isometry and define rotation and central symmetry. In third chapter we construct angle and we use 0 angle and straight angle as a base for comparison. To compare two angles we use relation ≤. Also, in this thesis we define supremum and infimum and sum of angles. In the end there is notion of measure of an angle and theorem that proves existence of that measure.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:273919
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 on2019-01-07 09:52:48