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undergraduate thesis
Trokutasti brojevi
2024. urn:nbn:hr:126:830944
Jurec, Matej
Josip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics

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Jurec, M. (2024). Trokutasti brojevi (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:830944

Jurec, Matej. "Trokutasti brojevi." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2024. https://urn.nsk.hr/urn:nbn:hr:126:830944

Jurec, Matej. "Trokutasti brojevi." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2024. https://urn.nsk.hr/urn:nbn:hr:126:830944

Jurec, M. (2024). 'Trokutasti brojevi', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, accessed 03 December 2024, https://urn.nsk.hr/urn:nbn:hr:126:830944

Jurec M. Trokutasti brojevi [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics; 2024 [cited 2024 December 03] Available at: https://urn.nsk.hr/urn:nbn:hr:126:830944

M. Jurec, "Trokutasti brojevi", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, Osijek, 2024. Available at: https://urn.nsk.hr/urn:nbn:hr:126:830944

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Metadata
TitleTrokutasti brojevi
Title (english)Triangular Numbers
AuthorMatej Jurec
MentorIvan Soldo (mentor)
GranterJosip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics
Osijek
Defense date and country2024-09-14, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Algebra
Abstract
Ovaj završni rad bavi se trokutastim brojevima koji su posebna vrsta figurativnih brojeva. Figurativne brojeve otkrili su još stari Grci te su se njima služili kako bi vizualno prikazali neke geometrijske oblike. Vidjeli smo da je n-ti trokutasti broj jednak sumi prvih n prirodnih brojeva. Odnosno, ako postoji cijeli broj t takav da je n = t(t+1)/2, kažemo da je n trokutasti broj. Osim primjena u teoriji brojeva postoje razne primjene trokutastih brojeva i u drugim područjima, dok su neke od najpoznatijih primjena one u kombinatorici, teoriji grafova, računarstvu i u fizici. Znamo da se trokutasti brojevi pojavljuju i u Pascalovom trokutu, kao i kod problema iz kombinatorike nazvanog problem rukovanja. U računarstvu kada tražimo kompleksnost nekog algoritma trokutasti brojevi će odigrati ključnu ulogu i olakšati nam razumijevanje složenosti tog algoritma. Ako se zaputimo odigrati partiju biljara ili na kuglanje primjetit ćemo vizualni oblik trokutastih brojeva u poziciji loptica odnosno čunjeva.
Abstract (english)
This final paper deals with triangular numbers, which are a special type of figurative numbers. Figurative numbers were discovered by the ancient Greeks, who used them to visually represent certain geometric shapes. We saw that the n-th triangular number is equal to the sum of the first n positive integers. In other words, if there is an integer t such that n = t(t+1)/2 , we say that n is a triangular number. Besides applications in number theory, triangular numbers have various applications in other fields, with some of the most well-known being in combinatorics,graph theory, computer science, and physics. We know that triangular numbers also appear in Pascal’s triangle and in combinatorial problems such as the handshake problem. In computer science, when determining the complexity of an algorithm, triangular numbers play a crucial role and help us understand the complexity of that algorithm. If we set out to play a game of billiards or bowling, we will notice the visual form of triangular numbers in the arrangement of the balls or pins.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:830944
Study programmeTitle: Bachelor of Mathematics and Computer Science
Study programme type: university
Study level: undergraduate
Academic / professional title: sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike i računarstva (sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike i računarstva)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2024-10-15 10:49:09