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master's thesis
Pitagorine trojke i neke slične diofantske jednadžbe
Zagreb: University of Zagreb, Faculty of Science, 2018. urn:nbn:hr:217:787487
Varga, Martina
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Varga, M. (2018). Pitagorine trojke i neke slične diofantske jednadžbe (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:787487

Varga, Martina. "Pitagorine trojke i neke slične diofantske jednadžbe." Master's thesis, University of Zagreb, Faculty of Science, 2018. https://urn.nsk.hr/urn:nbn:hr:217:787487

Varga, Martina. "Pitagorine trojke i neke slične diofantske jednadžbe." Master's thesis, University of Zagreb, Faculty of Science, 2018. https://urn.nsk.hr/urn:nbn:hr:217:787487

Varga, M. (2018). 'Pitagorine trojke i neke slične diofantske jednadžbe', Master's thesis, University of Zagreb, Faculty of Science, accessed 26 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:787487

Varga M. Pitagorine trojke i neke slične diofantske jednadžbe [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2018 [cited 2024 December 26] Available at: https://urn.nsk.hr/urn:nbn:hr:217:787487

M. Varga, "Pitagorine trojke i neke slične diofantske jednadžbe", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2018. Available at: https://urn.nsk.hr/urn:nbn:hr:217:787487

Metadata
TitlePitagorine trojke i neke slične diofantske jednadžbe
AuthorMartina Varga
MentorVedran Krčadinac (mentor)
Committee memberVedran Krčadinac (predsjednik povjerenstva)
Committee memberOzren Perše (član povjerenstva)
Committee memberNela Bosner (član povjerenstva)
Committee memberIlja Gogić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2018-09-26, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Pitagorine trojke su rješenja diofantske jednadžbe \(x^2+y^2=z^2\). Nakon kratkog povijesnog pregleda, u radu obrađujemo tri dokaza Euklidove formule za generiranje primitivnih Pitagorinih trojki. Osim navedene, proučavamo neke slične diofantske jednadžbe. Pitagorine četvorke su rješenja diofantske jednadžbe \(x^2+y^2+z^2=w^2\). Zatim prikazujemo parametrizirane formule za generiranje primitivnih Pitagorinih četvorki. Blizu Pitagorine trojke su rješenja diofantske jednadžbe \(x^2+y^2=z^2-1\), dok su skoro Pitagorine trojke rješenja diofantske jednadžbe \(x^2+y^2=z^2+1\). Pokazujemo vezu blizu i skoro Pitagorinih trojki s prethodnim jednadžbama te njihov međusobni odnos. Osim toga, u radu navodimo korake za generiranje skoro Pitagorinih trojki.
Abstract (english)
Pythagorean triples are solutions of the Diophantine equation \(x^2+y^2=z^2\). After a short historical review, we elaborate three proofs of Euclid’s formula for generating primitive Pythagorean triples. In addition, we study some similar Diophantine equations. Pythagorean quadruplets are solutions of the Diophantine equation \(x^2+y^2+z^2=w^2\). We present parameterized formulas for generating primitive Pythagorean quadruplets. Nearly Pythagorean triples are solutions of the Diophantine equation \(x^2+y^2=z^2-1\), while almost Pythagorean triples are solutions of the Diophantine equation \(x^2+y^2=z^2+1\). We show a close relationship between nearly and almost Pythagorean triples and their relation with the previous equations. In addition, we outline the steps for generating almost Pythagorean triples.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:787487
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
Embargo expiration date: 2019-10-03
Terms of useLicence In copyright icon
Created on2019-07-03 10:01:40