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master's thesis
Euklidov peti postulat
Zagreb: University of Zagreb, Faculty of Science, 2018. urn:nbn:hr:217:820483
Rašić, Mihaela
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Rašić, M. (2018). Euklidov peti postulat (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:820483

Rašić, Mihaela. "Euklidov peti postulat." Master's thesis, University of Zagreb, Faculty of Science, 2018. https://urn.nsk.hr/urn:nbn:hr:217:820483

Rašić, Mihaela. "Euklidov peti postulat." Master's thesis, University of Zagreb, Faculty of Science, 2018. https://urn.nsk.hr/urn:nbn:hr:217:820483

Rašić, M. (2018). 'Euklidov peti postulat', Master's thesis, University of Zagreb, Faculty of Science, accessed 03 May 2024, https://urn.nsk.hr/urn:nbn:hr:217:820483

Rašić M. Euklidov peti postulat [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2018 [cited 2024 May 03] Available at: https://urn.nsk.hr/urn:nbn:hr:217:820483

M. Rašić, "Euklidov peti postulat", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2018. Available at: https://urn.nsk.hr/urn:nbn:hr:217:820483

Metadata
TitleEuklidov peti postulat
AuthorMihaela Rašić
MentorFranka Miriam Bruckler (mentor)
Committee memberFranka Miriam Bruckler (predsjednik povjerenstva)
Committee memberNenad Antonić (član povjerenstva)
Committee memberSiniša Slijepčević (član povjerenstva)
Committee memberMea Bombardelli (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2018-07-16, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Euklid je uz Arhimeda i Apolonija bio jedan od najvećih antičkih grčkih matematičara. Najpoznatije Euklidovo djelo su Elementi, nastali oko 300. godine prije Krista. Elementi čine sintezu tad poznate matematike, oni su prvi pokušaj sustavne izgradnje geometrije pomoću deduktivne logičke metode. Euklid je sve svoje tvrdnje u Elementima izveo iz samo pet aksioma i pet postulata. Peti Euklidov postulat, poznat kao postulat o paralelama, najviše je kritiziran od strane drugih matematičara. Naime, zbog njegove složenosti pitalo se može li se on dokazati, odnosno je li on teorem ili stvarno postulat. Tijekom više od 2000 godina matematičari su pokušavali dokazati peti postulat i pritom su otkrivene mnoge njemu ekvivalentne tvrdnje. Konačno, u 19. stoljeću, ruski matematičar Nikolaj Ivanovič Lobačevski i mađarski János Bolyai prvi su izveli posljedice geometrije u kojoj on ne vrijedi, no time nije još bila potvrđena njegova nezavisnost od ostalih postulata. To je potvrdio model hiperbolične geometrije Eugenia Beltramija 1868.
Abstract (english)
Euclid, besides Archimedes and Appolonius, was one of the greatest ancient Greek mathematicians. He is best known for his Elements, dated about 300 BC. Elements are a synthesis of the mathematics of its time and they are the first attempt of developing geometry by strictly deductive logical reasoning. Euclid developed his geometry in Elements from five axioms and five postulates. His fifth postulate, known as the parallel postulate, was criticized by other mathematicians. Namely, because of its complexity, the question of it being a postulate or a theorem arose. In about 2000 years many attempts were made to prove it, which resulted in many equivalent formulations. Finally, in the 19th century, the Russian mathematician Nikolai Ivanovich Lobachevsky and the Hungarian János Bolyai described the consequences of a geometry in which this axiom is not valid. The independence of the parallel postulate was finally confirmed by Eugenio Beltrami’s first model of non-Euclidean (hyperbolic) geometry in 1868.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:820483
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 conditionsClosed access
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Created on2019-06-14 09:52:55