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undergraduate thesis
Diofantske aproksimacije
Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2024. urn:nbn:hr:126:479083
Kurtović, Dora
Josip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics

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Kurtović, D. (2024). Diofantske aproksimacije (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:479083

Kurtović, Dora. "Diofantske aproksimacije." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2024. https://urn.nsk.hr/urn:nbn:hr:126:479083

Kurtović, Dora. "Diofantske aproksimacije." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2024. https://urn.nsk.hr/urn:nbn:hr:126:479083

Kurtović, D. (2024). 'Diofantske aproksimacije', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, accessed 21 December 2024, https://urn.nsk.hr/urn:nbn:hr:126:479083

Kurtović D. Diofantske aproksimacije [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics; 2024 [cited 2024 December 21] Available at: https://urn.nsk.hr/urn:nbn:hr:126:479083

D. Kurtović, "Diofantske aproksimacije", 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:126:479083

Metadata
TitleDiofantske aproksimacije
Title (english)Diophantine Approximations
AuthorDora Kurtović
MentorMirela Jukić Bokun (mentor)
GranterJosip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics
Osijek
Defense date and country2024-09-30, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Other Mathematical Disciplines
Abstract
Tema ovog rada su diofantske aproksimacije. Na početku rada upoznajemo se s problemom aproksimacije iracionalnih brojeva racionalnim te ga proučavamo kroz Dirichletov teorem. Navodimo definicije i osnovna svojstva Fareyevih nizova te verižnih razlomaka, a zatim ih promatramo kao matematičke alate, s posebnim fokusom na njihovu ulogu u generiranju najtočnijih racionalnih aproksimacija. Drugi dio rada posvećen je aproksimaciji algebarskih i transcendentnih brojeva. Nakon što ih definiramo, navodimo dva ključna teorema za njihovu aproksimaciju, Liouvilleov i Rothov teorem.
Abstract (english)
This paper focuses on Diophantine approximations. It begins by addressing the challenge of approximating irrational numbers with rational ones, exploring Dirichlet’s theorem as a potential solution. The definitions and fundamental properties of Farey series and continued fractions are outlined and examined as mathematical tools, with special attention given to their role in generating the most accurate rational approximations. The second part of the paper delves into approximating algebraic and transcendental numbers, defining them and presenting two critical theorems for their approximation: Liouville’s and Roth’s theorems.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:479083
Study programmeTitle: University Bachelor of Mathematics (univ. bacc. math.)
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
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Created on2024-10-07 11:23:31