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master's thesis
Pitagorin poučak i njegove generalizacije
Zagreb: University of Zagreb, Faculty of Science, 2023. urn:nbn:hr:217:768386
Cifrek, Marta
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Cifrek, M. (2023). Pitagorin poučak i njegove generalizacije (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:768386

Cifrek, Marta. "Pitagorin poučak i njegove generalizacije." Master's thesis, University of Zagreb, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:217:768386

Cifrek, Marta. "Pitagorin poučak i njegove generalizacije." Master's thesis, University of Zagreb, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:217:768386

Cifrek, M. (2023). 'Pitagorin poučak i njegove generalizacije', Master's thesis, University of Zagreb, Faculty of Science, accessed 26 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:768386

Cifrek M. Pitagorin poučak i njegove generalizacije [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2023 [cited 2024 November 26] Available at: https://urn.nsk.hr/urn:nbn:hr:217:768386

M. Cifrek, "Pitagorin poučak i njegove generalizacije", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2023. Available at: https://urn.nsk.hr/urn:nbn:hr:217:768386

Metadata
TitlePitagorin poučak i njegove generalizacije
Title (english)Pythagorean theorem and its generalizations
AuthorMarta Cifrek
MentorRenata Vlahović Kruc (mentor)
Committee memberVedran Krčadinac (predsjednik povjerenstva)
Committee memberDražen Adamović (član povjerenstva)
Committee memberIgor Ciganović (član povjerenstva)
Committee memberSiniša Slijepčević (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2023-09-28, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu proučavali smo dobro poznat Pitagorin poučak. Poučak koji, prema nekim matematičarima, predstavlja početak suvremene matematike. U prvom dijelu istražili smo povijest Pitagore, Pitagorejske škole i Pitagorinog poučka te prikazali neke od preko 400 dokaza. Pritom smo razmatrali različite pristupe dokazivanju poučka. U drugom dijelu proučavali smo formulu kojom su određeni prirodni brojevi koji zadovoljavaju Pitagorin poučak, takozvane Pitagorine trojke. Potom smo poučak generalizirali na bilo koje medusobno slične likove nad stranicama pravokutnog trokuta, a zatim smo se bavili još nekim generalizacijama poučka u ravnini i prostoru. Na kraju se predlaže moguća realizacija Pitagorinog poučka i njegovog obrata u nastavi matematike.
Abstract (english)
In this thesis we studyed well known Pythagorean theorem. Theorem which, according to some mathematicians, represents the beginning of modern mathematics. The first part consist of the history of Pythagoras, Pythagoreanism, Pythagorean theorem and analysis of some of over 400 proofs of the theorem. Also, we studyed different approaches to prooving the theorem. The second part beggins with the formula that determines natural numbers that satisfy Pythagorean theorem, so called Pythagorean triples. Then we generalized the theorem to any similar figures on the sides of the right triangle and then we studyed another generalizations of the theorem in plane and in space. The final chapter suggests the possible realisation of Pythagorean theorem while teaching mathematics.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:768386
Study programmeTitle: Mathematics Education; specializations in: Mathematics Education
Course: Mathematics Education
Study programme type: university
Study level: graduate
Academic / professional title: sveučilišni magistar edukacije matematike (sveučilišni magistar edukacije matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2024-01-30 13:06:10