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Pitagorine trojke i njihova generalizacija
Ivana Penava (2016)
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics
Algebra and Calculus Research Group
Cite this document

Penava, I. (2016). Pitagorine trojke i njihova generalizacija (Undergraduate thesis). Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:815707

Penava, Ivana. "Pitagorine trojke i njihova generalizacija." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2016. https://urn.nsk.hr/urn:nbn:hr:126:815707

Penava, Ivana. "Pitagorine trojke i njihova generalizacija." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2016. https://urn.nsk.hr/urn:nbn:hr:126:815707

Penava, I. (2016). 'Pitagorine trojke i njihova generalizacija', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 04 April 2020, https://urn.nsk.hr/urn:nbn:hr:126:815707

Penava I. Pitagorine trojke i njihova generalizacija [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2016 [cited 2020 April 04] Available at: https://urn.nsk.hr/urn:nbn:hr:126:815707

I. Penava, "Pitagorine trojke i njihova generalizacija", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2016. Available at: https://urn.nsk.hr/urn:nbn:hr:126:815707

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Metadata
TitlePitagorine trojke i njihova generalizacija
Title (english)Pythagorean triples and their generalization
AuthorIvana Penava
MentorIvan Soldo (mentor)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Pure Mathematics)
(Algebra and Calculus Research Group)
Osijek
Defense date and country2016-09, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Glavna tema ovog rada su Pitagorine trojke, tj. trojke prirodnih brojeva koje su rješenje Pitagorine jednadžbe. U prvom poglavlju bavitćemo se definicijom i osnovnim svojstvima Pitagorinih trojki. Iskazat ćemo i dokazati Euklidov teorem kojim se one generiraju. Na kraju poglavlja na primjeru ćemo pokazati da je svaki prirodan broj član neke Pitagorine trojke. U drugom poglavlju obradit ćemo najvažnije teoreme vezane uz Pitagorine trojke. Kroz brojne primjere pokazat ćemo vezu Pitagorinih trojki s potpunim kvadratima cijeloga broja. Provjerit ćemo mogu li površine i duljine stranica Pitagorinih trokuta biti potpuni kvadrati. Nakon toga, obradit ćemo specifičnu vrstu trojki, s dvije ili tri uzastopne duljine stranica. Na kraju poglavlja istražit ćemo postoje li različiti Pitagorini trokuti iste površine. U posljednjem poglavlju susrest ćemo se s generalizacijom Pitagorinih trojki. Opisat ćemo način za generiranje svih Pitagorinih trojki (primitivnih i neprimitivnih), te s nekoliko primjera pokazati postupke njihova dobivanja.
Abstract (english)
The main topic of this thesis are Pythagorean triples, i.e., triples of positive integers satisfying the Pythagorean equation. In Section 1 we'll deal with denition and basic conditions of Pythagorean triples. We will show and prove Euclid's theorem for their generalization. At the end of rst section, we'll show that every positive integer is member of some Pythagorean triple. In Section 2 we will present the most important theorems associated with Pythagorean triples. By many examples we'll show connection between Pythagorean triples and perfect squares. We'll test whether areas and sides of Pythagorean triangles are perfect squares. Furthermore, we'll deal with their specic kind, where at least two sides are consecutive positive integers. Finally, we'll explore whether there exist dierent Pythagorean triangles with the same areas. In the last section we'll meet with generalization of Pythagorean triples. We'll describe a way to generate all Pythagorean triples (primitive and non-primitive), and in few examples show how to make them.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:815707
Study programmeTitle: University undergraduate study programme in mathematics
Study programme type: university
Study level: undergraduate
Academic / professional title: sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike (sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of usehttp://rightsstatements.org/vocab/InC/1.0/
Created on2016-10-04 09:58:43